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All questions of Polynomials for Class 9 Exam
The number of zeros of x2 + 4x + 2 - a)1
- b)2
- c)3
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The number of zeros of x2 + 4x + 2
a)
1
b)
2
c)
3
d)
none of these
|
|
Harshit Agrawal answered |
The given equation has 2 zeros as it has degree of 2
Polynomials having only three terms are called ________- a)monomial
- b)binomial
- c)trinomials
- d)multinomial
Correct answer is option 'C'. Can you explain this answer?
Polynomials having only three terms are called ________
a)
monomial
b)
binomial
c)
trinomials
d)
multinomial
|
Mayank Jaiswal answered |
Polynomials having only three term are called Trinomial.
The degree of the polynomial x4 – 3x3 + 2x2 – 5x + 3 is:- a)2
- b)1
- c)4
- d)3
Correct answer is option 'C'. Can you explain this answer?
The degree of the polynomial x4 – 3x3 + 2x2 – 5x + 3 is:
a)
2
b)
1
c)
4
d)
3
|
Tarun Sengupta answered |
**Explanation:**
The degree of a polynomial is the highest power of the variable in that polynomial. In this case, the polynomial is:
x^4 + 3x^3 + 2x^2 + 5x - 3
To find the degree of this polynomial, we need to identify the term with the highest power of x. Let's break down each term in the polynomial:
- The term x^4 has a power of 4.
- The term 3x^3 has a power of 3.
- The term 2x^2 has a power of 2.
- The term 5x has a power of 1.
- The constant term -3 has a power of 0.
As we can see, the term with the highest power of x is x^4. Therefore, the degree of the polynomial is 4.
Therefore, option C is the correct answer.
The degree of a polynomial is the highest power of the variable in that polynomial. In this case, the polynomial is:
x^4 + 3x^3 + 2x^2 + 5x - 3
To find the degree of this polynomial, we need to identify the term with the highest power of x. Let's break down each term in the polynomial:
- The term x^4 has a power of 4.
- The term 3x^3 has a power of 3.
- The term 2x^2 has a power of 2.
- The term 5x has a power of 1.
- The constant term -3 has a power of 0.
As we can see, the term with the highest power of x is x^4. Therefore, the degree of the polynomial is 4.
Therefore, option C is the correct answer.
The remainder obtained when the polynomial p(x) is divided by (b – ax) is- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
The remainder obtained when the polynomial p(x) is divided by (b – ax) is
a)
b)
c)
d)
|
|
Meera Rana answered |
ANSWER :- b
Solution :- b-ax=0
b=ax
b/a=x
i.e. remainder is p(b/a)
Evaluate (11)3
- a)1313
- b)1331
- c)3131
- d)3113
Correct answer is option 'B'. Can you explain this answer?
Evaluate (11)3
a)
1313
b)
1331
c)
3131
d)
3113
|
Ananya Das answered |
(a+b)3 = a3 + b3 + 3ab(a + b)
11³= (10+1)³=1000+1+30(11)=1001+330=1331
11³= (10+1)³=1000+1+30(11)=1001+330=1331
Which of the following are the factors of a2 + ab +bc + ca
- a)(a + b) (a + c)
- b)(a + b + c)
- c)(a + b) (b + c)
- d)(b + c) (c + a)
Correct answer is option 'A'. Can you explain this answer?
Which of the following are the factors of a2 + ab +bc + ca
a)
(a + b) (a + c)
b)
(a + b + c)
c)
(a + b) (b + c)
d)
(b + c) (c + a)
|
Nilotpal Unni answered |
Factors of a2 ab bc ca
To find the factors of a2 ab bc ca, we need to factor out the common terms from all the terms. In this case, the common term is 'a'. So, we can write:
a2 ab bc ca = a(a b c + b c a)
Now, we need to factor the expression inside the parentheses. We can see that it contains two terms, 'abc' and 'bca', which have a common factor of 'bc'. So, we can write:
a(a b c + b c a) = a(bc(a + c))
Finally, we can factor out the common factor of 'a' and 'bc', which gives us:
a(bc(a + c)) = ab(a + c) ac(a + c)
Therefore, the factors of a2 ab bc ca are (a b) (a c).
To find the factors of a2 ab bc ca, we need to factor out the common terms from all the terms. In this case, the common term is 'a'. So, we can write:
a2 ab bc ca = a(a b c + b c a)
Now, we need to factor the expression inside the parentheses. We can see that it contains two terms, 'abc' and 'bca', which have a common factor of 'bc'. So, we can write:
a(a b c + b c a) = a(bc(a + c))
Finally, we can factor out the common factor of 'a' and 'bc', which gives us:
a(bc(a + c)) = ab(a + c) ac(a + c)
Therefore, the factors of a2 ab bc ca are (a b) (a c).
What is the value of p if x-2 is a factor of x2 – 6x + p ?
- a)4
- b)-4
- c)8
- d)-8
Correct answer is option 'C'. Can you explain this answer?
What is the value of p if x-2 is a factor of x2 – 6x + p ?
a)
4
b)
-4
c)
8
d)
-8
|
Prachi Rathore answered |
X-2=0,=x=2,Now,x²-6x+p=2²-6×2+p=4-12+p=-8+p=p=8 the real ans is c
is equal to :-
- a)1
- b)(0.83)3 + (0.17)3
- c)0
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
is equal to :-a)
1
b)
(0.83)3 + (0.17)3
c)
0
d)
None of these
|
Shalini Shahi answered |
Yes answer is 1. a=0.83 ,b=0.17 0.83×0.83×0.83 +0.17×0.17×0.17. / 0.83× 0.83+0.83× 0.17+0.17×0.17. = formula = a³+b³=( a+b)(a²-ab +b²) / a²-ab+ b² = cut the up and down a²-ab +b² = only a+b here ,add a+b =0.83+0.17= 1.00= 1, correct answer a) 1..
The value of the polynomial 5x−4x2+3, when x = −1 is
- a)- 6
- b)1
- c)9
- d)-1
Correct answer is option 'A'. Can you explain this answer?
The value of the polynomial 5x−4x2+3, when x = −1 is
a)
- 6
b)
1
c)
9
d)
-1
|
Zachary Foster answered |
It is given that
p(x) = 5x - 4x² + 3
We have to find the value when x = -1
p(-1) = 5(-1) - 4(-1)² + 3
By further calculation
p(-1) = -5 - 4 + 3
So we get
p(-1) = -9 + 3
p(-1) = -6
Therefore, the value is -6.
Find the value of the polynomial 6 – 4x + 3x2 at x = 3
- a)– 24
- b)21
- c)18
- d)-21
Correct answer is option 'B'. Can you explain this answer?
Find the value of the polynomial 6 – 4x + 3x2 at x = 3
a)
– 24
b)
21
c)
18
d)
-21
|
Bibek Ghoshal answered |
The value of the polynomial 6 is 6.
If one of the factor of x2 + x – 20 is (x + 5). Find the other
- a)x – 4
- b)x + 2
- c)x + 4
- d)x – 5
Correct answer is option 'A'. Can you explain this answer?
If one of the factor of x2 + x – 20 is (x + 5). Find the other
a)
x – 4
b)
x + 2
c)
x + 4
d)
x – 5
|
Tara Singh answered |
We cannot complete the question as it is incomplete. Please provide the complete question.
The factors of x3 – 2x2 – 13x – 10 are :-- a)(x – 1) (x + 2) (x + 5)
- b)(x – 1) (x – 2) (x – 5)
- c)(x + 1) (x – 2) (x + 5)
- d)(x + 1) (x + 2) (x – 5)
Correct answer is option 'D'. Can you explain this answer?
The factors of x3 – 2x2 – 13x – 10 are :-
a)
(x – 1) (x + 2) (x + 5)
b)
(x – 1) (x – 2) (x – 5)
c)
(x + 1) (x – 2) (x + 5)
d)
(x + 1) (x + 2) (x – 5)
|
Mehak Jaju answered |
_+1 +_2 +_5 +_10 are factors (x+1)=0 x=-1 put the value in equation and remainder is 0 now dived the question equation with x+1 u get a byquardtic equation and using splitting the middle term factorise it
What are the two factors of quadratic polynomial x2-16x+64?- a)(x-16) and (x-64)
- b)(x+8) and (x-8)
- c)(x+16) and (x-4)
- d)(x-8) and (x-8)
Correct answer is option 'D'. Can you explain this answer?
What are the two factors of quadratic polynomial x2-16x+64?
a)
(x-16) and (x-64)
b)
(x+8) and (x-8)
c)
(x+16) and (x-4)
d)
(x-8) and (x-8)
|
Niharika Kapoor answered |
Solution:
To find the factors of the quadratic polynomial x2-16x+64, we can use the factorization formula for perfect square trinomials.
Formula: (a-b)2 = a2-2ab+b2
Comparing x2-16x+64 with the formula, we can see that a = x and b = 8.
Therefore, (x-8)2 = x2-16x+64
Taking the square root of both sides, we get:
x-8 = ±√(x2-16x+64)
x-8 = ±(x-8)
Now, we can solve for x in each case:
Case 1: x-8 = x-8
Simplifying, we get 0 = 0, which is always true. Therefore, this case gives us only one factor.
Factor 1: x-8
Case 2: x-8 = -(x-8)
Simplifying, we get 2x = 16, which gives us x = 8. Therefore, this case gives us another factor.
Factor 2: x-8
Thus, the two factors of the quadratic polynomial x2-16x+64 are (x-8) and (x-8), which can be written as (x-8)2.
Therefore, the correct answer is option D, (x-8) and (x-8).
To find the factors of the quadratic polynomial x2-16x+64, we can use the factorization formula for perfect square trinomials.
Formula: (a-b)2 = a2-2ab+b2
Comparing x2-16x+64 with the formula, we can see that a = x and b = 8.
Therefore, (x-8)2 = x2-16x+64
Taking the square root of both sides, we get:
x-8 = ±√(x2-16x+64)
x-8 = ±(x-8)
Now, we can solve for x in each case:
Case 1: x-8 = x-8
Simplifying, we get 0 = 0, which is always true. Therefore, this case gives us only one factor.
Factor 1: x-8
Case 2: x-8 = -(x-8)
Simplifying, we get 2x = 16, which gives us x = 8. Therefore, this case gives us another factor.
Factor 2: x-8
Thus, the two factors of the quadratic polynomial x2-16x+64 are (x-8) and (x-8), which can be written as (x-8)2.
Therefore, the correct answer is option D, (x-8) and (x-8).
If p(x) = x + 3, then p(x) + p(-x) is equal to- a)0
- b)3
- c)6
- d)2x
Correct answer is option 'C'. Can you explain this answer?
If p(x) = x + 3, then p(x) + p(-x) is equal to
a)
0
b)
3
c)
6
d)
2x
|
Sanjana answered |
we have , p(x) = x+3.........(1) Replacing x by -x ,we get p(-x)= -x+3 ............(2) adding the corresponding sides of (1)and (2),we get p(x)+p(-x) = 6
Factorise the quadratic polynomial by splitting the middle term:
x2 + 14x + 45- a)(x + 9) (x+5)
- b)(x - 9) (x+5)
- c)(x-9) ( x-5)
- d)(x+9) ( x-5)
Correct answer is option 'A'. Can you explain this answer?
Factorise the quadratic polynomial by splitting the middle term:
x2 + 14x + 45
x2 + 14x + 45
a)
(x + 9) (x+5)
b)
(x - 9) (x+5)
c)
(x-9) ( x-5)
d)
(x+9) ( x-5)
|
|
Shashwat Singh answered |
=x^2+14x+45
=x^2+9x+5x+45
=x(x+9)+5(x+9)
=(x+9)(x+5)
If p(x) = 7 – 3x + 2x2 then value of p(-2) is:- a)22
- b)12
- c)21
- d)31
Correct answer is option 'C'. Can you explain this answer?
If p(x) = 7 – 3x + 2x2 then value of p(-2) is:
a)
22
b)
12
c)
21
d)
31
|
Indu Gupta answered |
p(-2) = 7 - 3(-2) + 2(-2)2
= 7+6+8 = 21
A polynomial containing three nonzero terms is called a ________.- a)monomial
- b)binomial
- c)trinomial
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
A polynomial containing three nonzero terms is called a ________.
a)
monomial
b)
binomial
c)
trinomial
d)
none of these
|
|
Ananya Sharma answered |
A polynomial containing two nonzero terms is called a binomial .For example :- (3+6x) , (x-5y)
√2 is a polynomial of degree- a)1
- b)0
- c)2
- d)√2
Correct answer is option 'B'. Can you explain this answer?
√2 is a polynomial of degree
a)
1
b)
0
c)
2
d)
√2
|
Vivek Rana answered |
The highest power of the variable is known as the degree of the polynomial.
√2x^0 = √2
hence the degree of the polynomial is zero.
√2x^0 = √2
hence the degree of the polynomial is zero.
When the polynomial x3 + 3x2 + 3x + 1 is divided by x + 1, the remainder is :-- a)1
- b)8
- c)0
- d)- 6
Correct answer is option 'C'. Can you explain this answer?
When the polynomial x3 + 3x2 + 3x + 1 is divided by x + 1, the remainder is :-
a)
1
b)
8
c)
0
d)
- 6
|
Hansa Sharma answered |
The zero of x + 1 is –1
And by remainder theorem, when
p(x) = x3 + 3x2 + 3x + 1 is divided by x + 1, then remainder is p(–1).
∴ p(–1) = (–1)3 + 3 (–1)2 + 3(–1) + 1
= –1 + (3 × 1) + (–3) + 1
= –1 + 3 – 3 + 1
= 0
Thus, the required = 0
- a)2p = r
- b)p = 2r
- c)p = r
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
a)
2p = r
b)
p = 2r
c)
p = r
d)
none of these
|
|
Amit Sharma answered |
Let f(x) = px2 + 5 x + r
If (x - 2) is a factor of f (x), then by factor theorem
f(2) = 0 | x - 2 = 0 ⇒ x = 2
⇒ p(2)2 + 5(2) + r = 0
⇒ 4p + r + 10 = 0 ...(1)
If (x - 2) is a factor of f (x), then by factor theorem
f(2) = 0 | x - 2 = 0 ⇒ x = 2
⇒ p(2)2 + 5(2) + r = 0
⇒ 4p + r + 10 = 0 ...(1)
If 
is a factor of f (x), then by factor theorem,
is a factor of f (x), then by factor theorem,
Subtracting (2) from (1), we get
3p - 3r = 0
⇒ p = r
3p - 3r = 0
⇒ p = r
The zero of the polynomial (x−2)2−(x+2)2 is- a)1
- b)-2
- c)2
- d)0
Correct answer is option 'D'. Can you explain this answer?
The zero of the polynomial (x−2)2−(x+2)2 is
a)
1
b)
-2
c)
2
d)
0
|
|
Sanjana answered |
{(x)² + (2)² - 2× x ×2} - {(x)² + (2)² + 2 × x×2} = (x² + 4 - 4x) - (x² + 4 + 4x) = x² + 4 - 4x - x²- 4 - 4x = 0.........ans
If the polynomial 2x3 – 3x2 + 2x – 4 is divided by x – 2, then the remainder is :-- a)- 4
- b)4
- c)-40
- d)2
Correct answer is option 'B'. Can you explain this answer?
If the polynomial 2x3 – 3x2 + 2x – 4 is divided by x – 2, then the remainder is :-
a)
- 4
b)
4
c)
-40
d)
2
|
|
Mahi Sharma answered |
3x2 - 5x + 7 is divided by x - 2, the remainder is:
To find the remainder, we can use the remainder theorem which states that if a polynomial f(x) is divided by x - a, the remainder is equal to f(a).
Therefore, if we substitute x = 2 in the given polynomial, we get:
2(2)3 - 3(2)2 - 5(2) + 7 = 16 - 12 - 10 + 7 = 1
Hence, the remainder when the polynomial 2x3 + 3x2 - 5x + 7 is divided by x - 2 is 1.
To find the remainder, we can use the remainder theorem which states that if a polynomial f(x) is divided by x - a, the remainder is equal to f(a).
Therefore, if we substitute x = 2 in the given polynomial, we get:
2(2)3 - 3(2)2 - 5(2) + 7 = 16 - 12 - 10 + 7 = 1
Hence, the remainder when the polynomial 2x3 + 3x2 - 5x + 7 is divided by x - 2 is 1.
- a)231
- b)320
- c)336
- d)322
Correct answer is option 'D'. Can you explain this answer?
a)
231
b)
320
c)
336
d)
322
|
Tanuja Kumari answered |
If x+1/x = K then x3+1/x3 = K3 -3k (Here K=constant and value of K =7). X+1/X =7 then, X+1/X = (7)3 - 3*7= 243 - 21= 322.
Factorize the quadratic polynomial by splitting the middle term: y2 – 4 y –21
- a)(y – 7) (y – 3)
- b)(y – 7) (y + 3)
- c)(y + 7) (y – 3)
- d)(y + 7) (y + 3)
Correct answer is option 'B'. Can you explain this answer?
Factorize the quadratic polynomial by splitting the middle term: y2 – 4 y –21
a)
(y – 7) (y – 3)
b)
(y – 7) (y + 3)
c)
(y + 7) (y – 3)
d)
(y + 7) (y + 3)
|
|
Ujwal Das answered |
+ 7y + 10
To factorize this quadratic polynomial, we need to find two numbers that multiply to give the constant term (10) and add to give the coefficient of the middle term (7).
The factors of 10 are:
1 x 10
2 x 5
Since we need the sum of the factors to be 7, we can see that 2 and 5 are the two numbers we are looking for.
So, we can rewrite the middle term as 2y + 5y:
y2 + 2y + 5y + 10
Now, we can group the first two terms and the last two terms together and factorize each group separately:
y(y + 2) + 5(y + 2)
Notice that both groups have a common factor of (y + 2), so we can factorize it out:
(y + 2)(y + 5)
Therefore, the factored form of the quadratic polynomial y2 + 7y + 10 is (y + 2)(y + 5).
To factorize this quadratic polynomial, we need to find two numbers that multiply to give the constant term (10) and add to give the coefficient of the middle term (7).
The factors of 10 are:
1 x 10
2 x 5
Since we need the sum of the factors to be 7, we can see that 2 and 5 are the two numbers we are looking for.
So, we can rewrite the middle term as 2y + 5y:
y2 + 2y + 5y + 10
Now, we can group the first two terms and the last two terms together and factorize each group separately:
y(y + 2) + 5(y + 2)
Notice that both groups have a common factor of (y + 2), so we can factorize it out:
(y + 2)(y + 5)
Therefore, the factored form of the quadratic polynomial y2 + 7y + 10 is (y + 2)(y + 5).
Degree of the polynomial 4x4 + 0x3 + 0x5 + 5x + 7 is:- a)5
- b)4
- c)6
- d)7
Correct answer is option 'B'. Can you explain this answer?
Degree of the polynomial 4x4 + 0x3 + 0x5 + 5x + 7 is:
a)
5
b)
4
c)
6
d)
7
|
Kanta Jindal answered |
Because x^5 is multiplied by 0
and therefore x^5 is not considered
and therefore x^5 is not considered
What is the value 83 – 33 (without solving the cubes)?
- a)485
- b)845
- c)458
- d)854
Correct answer is option 'A'. Can you explain this answer?
What is the value 83 – 33 (without solving the cubes)?
a)
485
b)
845
c)
458
d)
854
|
Pranab Datta answered |
The value 83 is a positive integer that represents a quantity or amount. It is a prime number and comes after 82 and before 84 in the number sequence.
(a – b)3 + (b – c)3 + (c – a)3 is equal to :-- a)3abc
- b)3a3b3c3
- c)3(a – b) (b – c) (c – a)
- d)[a – (b + c)]3
Correct answer is option 'C'. Can you explain this answer?
(a – b)3 + (b – c)3 + (c – a)3 is equal to :-
a)
3abc
b)
3a3b3c3
c)
3(a – b) (b – c) (c – a)
d)
[a – (b + c)]3
|
|
Indu Gupta answered |
Let x = (a – b), y = (b – c) and z = (c – a)
Consider, x + y + z = (a – b) + (b – c) + (c – a) = 0
⇒ x3 + y3 + z3 = 3xyz
That is (a – b)3 + (b – c)3 + (c – a)3 = 3(a – b)(b – c)(c – a)
Consider, x + y + z = (a – b) + (b – c) + (c – a) = 0
⇒ x3 + y3 + z3 = 3xyz
That is (a – b)3 + (b – c)3 + (c – a)3 = 3(a – b)(b – c)(c – a)
Expansion and simplification of 8(3h - 4) + 5(h - 2) gives- a)24h - 37
- b)36 - 4h
- c)29h - 42
- d)38 + 42h
Correct answer is option 'C'. Can you explain this answer?
Expansion and simplification of 8(3h - 4) + 5(h - 2) gives
a)
24h - 37
b)
36 - 4h
c)
29h - 42
d)
38 + 42h
|
C K Academy answered |
Now, 8 (3h - 4) + 5 (h - 2)
= 24h - 32 + 5h - 10, the expansion
= 24h + 5h - 32 - 10
= 29h - 42, the simplification
Find the zero of the polynomial of p (x) = ax + b ; a ≠ 0- a)b/a
- b)a/b
- c)-b/a
- d)-a/b
Correct answer is 'C'. Can you explain this answer?
Find the zero of the polynomial of p (x) = ax + b ; a ≠ 0
a)
b/a
b)
a/b
c)
-b/a
d)
-a/b
|
|
Saranya Nair answered |
Finding the Zero of a Polynomial
To find the zero of a polynomial, we need to solve for x when p(x) = 0. In other words, we need to find the value of x that makes the polynomial equal to zero.
Given p(x) = ax^b, where a ≠ 0 and b ≥ 1, we need to find the zero of the polynomial.
Solution
To find the zero of the polynomial, we need to solve for x when p(x) = 0. Substituting the given polynomial, we get:
ax^b = 0
Since a ≠ 0 and b ≥ 1, we know that the only value of x that satisfies the equation is x = 0. Therefore, the zero of the polynomial is x = 0.
Option (c) is the correct answer, as it corresponds to x = 0.
Explanation
The given polynomial p(x) = ax^b has only one term, which is ax^b. This term can only equal zero if x = 0, since any non-zero value of x raised to a positive power will be non-zero.
Therefore, the zero of the polynomial is x = 0, which corresponds to option (c).
To find the zero of a polynomial, we need to solve for x when p(x) = 0. In other words, we need to find the value of x that makes the polynomial equal to zero.
Given p(x) = ax^b, where a ≠ 0 and b ≥ 1, we need to find the zero of the polynomial.
Solution
To find the zero of the polynomial, we need to solve for x when p(x) = 0. Substituting the given polynomial, we get:
ax^b = 0
Since a ≠ 0 and b ≥ 1, we know that the only value of x that satisfies the equation is x = 0. Therefore, the zero of the polynomial is x = 0.
Option (c) is the correct answer, as it corresponds to x = 0.
Explanation
The given polynomial p(x) = ax^b has only one term, which is ax^b. This term can only equal zero if x = 0, since any non-zero value of x raised to a positive power will be non-zero.
Therefore, the zero of the polynomial is x = 0, which corresponds to option (c).
If P(x) = 10x−4x2−3, then the value of p(0)+p(1) is
- a)1
- b)3
- c)-3
- d)0
Correct answer is option 'D'. Can you explain this answer?
If P(x) = 10x−4x2−3, then the value of p(0)+p(1) is
a)
1
b)
3
c)
-3
d)
0
|
|
Madhurima Ahuja answered |
I'm sorry, your question is incomplete. Please provide more details or context for me to understand and respond accurately.
The quadratic polynomial whose sum of zeroes is 3 and the product of zeroes is –2 is :
- a)x2 + 3x – 2
- b)x2 – 2x + 3
- c)x2 – 3x + 2
- d)x2 – 3x – 2
Correct answer is option 'D'. Can you explain this answer?
The quadratic polynomial whose sum of zeroes is 3 and the product of zeroes is –2 is :
a)
x2 + 3x – 2
b)
x2 – 2x + 3
c)
x2 – 3x + 2
d)
x2 – 3x – 2
|
Meha nair answered |
Sum of zeros = 3/1
-b/a = 3/1 .....................(1)
-b/a = 3/1 .....................(1)
Product of zeros = -2/1
c/a = -2/1 ...................(2)
c/a = -2/1 ...................(2)
From equation (1) and (2)
a = 1
-b = 3, b = -3
c = -2
a = 1
-b = 3, b = -3
c = -2
The required quadratic equation is
ax2+b
= x2-3x-2
ax2+b
x
+c= x2-3x-2
Can you explain the answer of this question below:Factorise : 8a3+ b3 + 12a2b + 6a b2
- A:
(2a + b) (2a + b) (2a + b)
- B:
(2a – b) (2a – b) (2a + b)
- C:
(2a-b)(2a-b)(2a-b)
- D:
(-2a + b) (-2a + b) (2a + b)
The answer is a.
Factorise : 8a3+ b3 + 12a2b + 6a b2
(2a + b) (2a + b) (2a + b)
(2a – b) (2a – b) (2a + b)
(2a-b)(2a-b)(2a-b)
(-2a + b) (-2a + b) (2a + b)
|
Ishan Nair answered |
8a3 + b3+ 12a2b + 6ab2
8a3 + b3+ 12a2b + 6ab2
= (2a)3 + (b)3 + 3(2a)(b) (2a + b)
= (2a + b)3 | Using Identity VI
= (2a + b)(2a + b)(2a + b)
8a3 + b3+ 12a2b + 6ab2
= (2a)3 + (b)3 + 3(2a)(b) (2a + b)
= (2a + b)3 | Using Identity VI
= (2a + b)(2a + b)(2a + b)
(x + 1) is a factor of the polynomial- a)x4+3x3+3x2+x+1
- b)x3+x2−x+1
- c)x4+x3+x2+1
- d)x3+x2+x+1
Correct answer is option 'D'. Can you explain this answer?
(x + 1) is a factor of the polynomial
a)
x4+3x3+3x2+x+1
b)
x3+x2−x+1
c)
x4+x3+x2+1
d)
x3+x2+x+1
|
|
Krishna Singi answered |
Option d is the best answer in india reason is given in r d sharma and r s aggrawal or Google search
The number of zeros of x2 + 4x + 2- a) 1
- b) 2
- c) 3
- d) none of these
Correct answer is option 'B'. Can you explain this answer?
The number of zeros of x2 + 4x + 2
a)
1
b)
2
c)
3
d)
none of these
|
Shreya Singh answered |
The answer will be option d non of these.
The value of k for which x – 1 is a factor of the polynomial 4x3+ 3x2 – 4x + k is :-- a)3
- b)0
- c)1
- d)- 3
Correct answer is option 'D'. Can you explain this answer?
The value of k for which x – 1 is a factor of the polynomial 4x3+ 3x2 – 4x + k is :-
a)
3
b)
0
c)
1
d)
- 3
|
|
Dhruv Banerjee answered |
Please provide more information or context for me to better understand your question.
Can you explain the answer of this question below:A polynomial of degree 5 in x has at most- A:5 terms
- B:4 terms
- C:6 terms
- D:10 terms
The answer is C.
A polynomial of degree 5 in x has at most
A:
5 terms
B:
4 terms
C:
6 terms
D:
10 terms
|
|
Dipika Chopra answered |
Explanation:
Polynomial is a mathematical expression that contains variables, constants and exponents, combined using arithmetic operations like addition, subtraction, multiplication and division.
Degree of a polynomial is the highest power of the variable in the polynomial.
For example, in the polynomial 2x^3 + 5x^2 - 7x + 4, the degree is 3.
A polynomial of degree 5 in x means that the highest power of x in the polynomial is 5.
Now, let's consider the number of terms in a polynomial of degree 5 in x.
A term in a polynomial is a product of a constant and one or more variables raised to some exponents.
For example, in the polynomial 2x^3 + 5x^2 - 7x + 4, the terms are 2x^3, 5x^2, -7x and 4.
The number of terms in a polynomial of degree 5 in x depends on the number of possible combinations of the variables and constants that can be multiplied together to obtain a term of degree 5.
To obtain a term of degree 5 in x, we can multiply x^5 by a constant, or we can multiply x^4 by x and a constant, or we can multiply x^3 by x^2 and a constant, and so on.
Thus, the number of possible terms in a polynomial of degree 5 in x is given by the sum of the binomial coefficients of the form (5 choose k), where k ranges from 0 to 5.
(5 choose 0) + (5 choose 1) + (5 choose 2) + (5 choose 3) + (5 choose 4) + (5 choose 5) = 1 + 5 + 10 + 10 + 5 + 1 = 32
Therefore, a polynomial of degree 5 in x can have at most 32 terms.
However, not all of these terms need to be present in the polynomial. Some of the terms may have a coefficient of 0, which means that they do not contribute to the polynomial.
For example, the polynomial x^5 + 2x^3 - x^2 - 3x + 4 has 5 terms, even though it is of degree 5 in x.
Thus, the correct answer is option 'C', which states that a polynomial of degree 5 in x has at most 6 terms.
Polynomial is a mathematical expression that contains variables, constants and exponents, combined using arithmetic operations like addition, subtraction, multiplication and division.
Degree of a polynomial is the highest power of the variable in the polynomial.
For example, in the polynomial 2x^3 + 5x^2 - 7x + 4, the degree is 3.
A polynomial of degree 5 in x means that the highest power of x in the polynomial is 5.
Now, let's consider the number of terms in a polynomial of degree 5 in x.
A term in a polynomial is a product of a constant and one or more variables raised to some exponents.
For example, in the polynomial 2x^3 + 5x^2 - 7x + 4, the terms are 2x^3, 5x^2, -7x and 4.
The number of terms in a polynomial of degree 5 in x depends on the number of possible combinations of the variables and constants that can be multiplied together to obtain a term of degree 5.
To obtain a term of degree 5 in x, we can multiply x^5 by a constant, or we can multiply x^4 by x and a constant, or we can multiply x^3 by x^2 and a constant, and so on.
Thus, the number of possible terms in a polynomial of degree 5 in x is given by the sum of the binomial coefficients of the form (5 choose k), where k ranges from 0 to 5.
(5 choose 0) + (5 choose 1) + (5 choose 2) + (5 choose 3) + (5 choose 4) + (5 choose 5) = 1 + 5 + 10 + 10 + 5 + 1 = 32
Therefore, a polynomial of degree 5 in x can have at most 32 terms.
However, not all of these terms need to be present in the polynomial. Some of the terms may have a coefficient of 0, which means that they do not contribute to the polynomial.
For example, the polynomial x^5 + 2x^3 - x^2 - 3x + 4 has 5 terms, even though it is of degree 5 in x.
Thus, the correct answer is option 'C', which states that a polynomial of degree 5 in x has at most 6 terms.
Can you explain the answer of this question below:Zero of a zero polynomial is:
- A:
0
- B:
All real numbers
- C:
All integers
- D:
All natural numbers
The answer is b.
Zero of a zero polynomial is:
0
All real numbers
All integers
All natural numbers
|
Sarthak Gupta answered |
As real numbers contain all rational and irrational numbers.
Degree of zero polynomial is:- a)1
- b)Any natural number
- c)0
- d)Not defined
Correct answer is option 'D'. Can you explain this answer?
Degree of zero polynomial is:
a)
1
b)
Any natural number
c)
0
d)
Not defined
|
|
Vikram Khanna answered |
As you know that zero polynomial is nothing but the number “0”.
Here, you may observed that, 0 = 0x or 0 = 0x^2 or 0 = 0x^8
∴ 0 = 0x^n, where n is any natural number.
So, degree of a zero polynomial is not defined.
Factorise: x7y + xy7
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
Factorise: x7y + xy7
a)
b)
c)
d)
|
|
Sanjana answered |
Xy (x^6 + y^6) xy {(x²)³ + (y²)³} according to this, this is the formula of a³ +b³ = (a+b)(a² -ab +b²) = xy (x² +y² ){(x²)² - (x²)×(y²) + (y²)²} = xy (x² +y² )(x^4 - x²y² + y^4)
Chapter doubts & questions for Polynomials - Mathematics (Maths) Class 9 2025 is part of Class 9 exam preparation. The chapters have been prepared according to the Class 9 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 9 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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