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All questions of Factorisation for Class 8 Exam
Factorise: x2+ 8x + 16- a)(x+ 3)2
- b)(x+ 2)2
- c)(x+ 4)2
- d)(x+ 5)2
Correct answer is option 'C'. Can you explain this answer?
Factorise: x2+ 8x + 16
a)
(x+ 3)2
b)
(x+ 2)2
c)
(x+ 4)2
d)
(x+ 5)2
 | Geetika Shah answered |
C ) (x2 +8x +16)
= (x2 + 4x + 4x + 16)
= ( x2 + 4x ) + (4x + 16 )
= x(x + 4 ) +4(x + 4 )
=(x + 4)(x + 4)
=(x + 4)2
= (x2 + 4x + 4x + 16)
= ( x2 + 4x ) + (4x + 16 )
= x(x + 4 ) +4(x + 4 )
=(x + 4)(x + 4)
=(x + 4)2
Solve: 7x2y2z2÷14xyza)(1/2)xyzb)(3/2)xyzc)(3/4)xyzd)(2/1)xyzCorrect answer is option 'A'. Can you explain this answer?
 | Target Study Academy answered |
7x²y²z²÷14xyz
=(7/14)(x²/x)(y²/y)(z²/z)
=1/2(x)(y)(z)
=1/2xyz.
=(7/14)(x²/x)(y²/y)(z²/z)
=1/2(x)(y)(z)
=1/2xyz.
Factorise: x2+x y+ 8x+ 8y- a)(x + 8) (x + y)
- b)(x + y)
- c)(x + 8)
- d)(x + 9) (x – y)
Correct answer is option 'A'. Can you explain this answer?
Factorise: x2+x y+ 8x+ 8y
a)
(x + 8) (x + y)
b)
(x + y)
c)
(x + 8)
d)
(x + 9) (x – y)
 | Aditi Saxena answered |
x^2 + xy + 8x + 8y = x[x + y] + 8[x + y]
= (x + y)(x + 8)
What are the factors of ax+by+bx+az+ay+bz?- a)(bx+ay),(ax+by)
- b)(a+b),(2x+2y+2z)
- c)(x+y+z),(a+b)
- d)(x+y−z),(a−b)
Correct answer is option 'C'. Can you explain this answer?
What are the factors of ax+by+bx+az+ay+bz?
a)
(bx+ay),(ax+by)
b)
(a+b),(2x+2y+2z)
c)
(x+y+z),(a+b)
d)
(x+y−z),(a−b)
| | Geetika Shah answered |
ax+by+bx+az+ay+bz, rearranging we get ax+ay+az+bx+by+bz
a(x+y+z)+b(x+y+z)=(a+b)(x+y+z). Hence the factors are (a+b), (x+y+z)
a(x+y+z)+b(x+y+z)=(a+b)(x+y+z). Hence the factors are (a+b), (x+y+z)
Divide the given polynomial by the given monomial: (x3+ 2x2+ 3x) ÷ 2x- a)1/2 (x2+2x+3)
- b)1/2
- c)(x2+2x+3)
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Divide the given polynomial by the given monomial: (x3+ 2x2+ 3x) ÷ 2x
a)
1/2 (x2+2x+3)
b)
1/2
c)
(x2+2x+3)
d)
none of these
| | Ananya Das answered |
(x3+2x2+3x)/2x
=x(x2+2x+3)/2x
=(x2+2x+3)/2
=x(x2+2x+3)/2x
=(x2+2x+3)/2
Find the common factors of 2y, 22xy.- a)2y
- b)2
- c)22
- d)y
Correct answer is option 'A'. Can you explain this answer?
Find the common factors of 2y, 22xy.
a)
2y
b)
2
c)
22
d)
y
| | Amit Sharma answered |
Only 2y is common in both the terms
Factorize x² + 8x + 12- a)(x + 2)(x + 6)
- b)(x + 3)(x + 4)
- c)3x + 12
- d)3x - 12
Correct answer is option 'A'. Can you explain this answer?
Factorize x² + 8x + 12
a)
(x + 2)(x + 6)
b)
(x + 3)(x + 4)
c)
3x + 12
d)
3x - 12
 | Kaavya Saha answered |
x² + 8x + 12
two no whose product is 12 and sum is 8
ie. 2 and 6 so;
x2+2x+6x+12
x(x+2)+6(x+2)
(x+2)(x+6)
two no whose product is 12 and sum is 8
ie. 2 and 6 so;
x2+2x+6x+12
x(x+2)+6(x+2)
(x+2)(x+6)
What are the factors of x4+2x2+9?- a)(x2+2x+3), (x2−2x+3)
- b)(x2+3), (x2−3)
- c)(x2+2x+3), (x2+2x+3)
- d)(x2+3), (x2+3)
Correct answer is option 'A'. Can you explain this answer?
What are the factors of x4+2x2+9?
a)
(x2+2x+3), (x2−2x+3)
b)
(x2+3), (x2−3)
c)
(x2+2x+3), (x2+2x+3)
d)
(x2+3), (x2+3)
 | Trisha Vashisht answered |
Given equation is x4 + 2x2 + 9
We can rewrite this as,
(x2)2 + 6x2 + 9 − 4x2
⇒ (x2 + 3)2 − (2x)2
....Since a2 + 2ab + b2 = (a+b)2
⇒ x4 + 2x2 + 9 = (x2 − 2x + 3)(x2 + 2x + 3)
....Since a2 − b2 = (a+b)(a−b)
We can rewrite this as,
(x2)2 + 6x2 + 9 − 4x2
⇒ (x2 + 3)2 − (2x)2
....Since a2 + 2ab + b2 = (a+b)2
⇒ x4 + 2x2 + 9 = (x2 − 2x + 3)(x2 + 2x + 3)
....Since a2 − b2 = (a+b)(a−b)
Which of the following is quotient obtained on dividing –18 xyz2 by –3 xz?- a)6 Yz
- b)–6 yz
- c)6 xy2
- d)6 xy
Correct answer is option 'A'. Can you explain this answer?
Which of the following is quotient obtained on dividing –18 xyz2 by –3 xz?
a)
6 Yz
b)
–6 yz
c)
6 xy2
d)
6 xy
| | Geetika Shah answered |
–18 xyz2/–3 xz x and x gets cancelled,-18 gets divided by -3 .and z2 gets divided by z so only one z remain in numerator So the quotient obtained is 6yz
Can you explain the answer of this question below:Divide as directed: 26xy (x + 5) (y – 4) ÷ 13x (y – 4)
- A:
2y (x + 5)
- B:
(x + 5)
- C:
2y
- D:
None of these
The answer is A.
Divide as directed: 26xy (x + 5) (y – 4) ÷ 13x (y – 4)
2y (x + 5)
(x + 5)
2y
None of these
 | Kavya Saxena answered |
26xy(x + 5) (y - 4) / 13x(y - 4)
Cancelling 13x(y-4)
=2y(x+5)
Cancelling 13x(y-4)
=2y(x+5)
What is the coefficient of 'a' when 9a2+18a is divided by (a+2)?- a)18
- b)9
- c)1/2
- d)2
Correct answer is option 'B'. Can you explain this answer?
What is the coefficient of 'a' when 9a2+18a is divided by (a+2)?
a)
18
b)
9
c)
1/2
d)
2
| | Gaurav Mukherjee answered |
Coefficient of a when 9a^2 - 18a is divided by (a - 2)
To find the coefficient of a, we need to perform long division as shown below:
9a - 18
(a - 2) | 9a^2 + 0a - 18
9a^2 - 18a
------------
18a - 18
18a - 36
--------
18
Therefore, the remainder is 18 and the quotient is 9a + 18. The coefficient of a in the quotient is 9, so the answer is option B) 9.
To find the coefficient of a, we need to perform long division as shown below:
9a - 18
(a - 2) | 9a^2 + 0a - 18
9a^2 - 18a
------------
18a - 18
18a - 36
--------
18
Therefore, the remainder is 18 and the quotient is 9a + 18. The coefficient of a in the quotient is 9, so the answer is option B) 9.
How many factors does (x9−x) have?- a)9
- b)4
- c)2
- d)5
Correct answer is option 'D'. Can you explain this answer?
How many factors does (x9−x) have?
a)
9
b)
4
c)
2
d)
5
 | Vivek Rana answered |
f(x) = x9- x
The degree of f(x) = 9
So , this polynomial will have 9 zeros
therefore it will have 9 factors
The degree of f(x) = 9
So , this polynomial will have 9 zeros
therefore it will have 9 factors
Factorise: p4– 81- a)(p – 3) (p + 3) (p2+ 9)
- b)(p + 3) (p2+ 9)
- c)(p – 3) (p + 3)
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Factorise: p4– 81
a)
(p – 3) (p + 3) (p2+ 9)
b)
(p + 3) (p2+ 9)
c)
(p – 3) (p + 3)
d)
none of these
 | Malavika Basu answered |
We have p4 - 81 = (p2)2 - (9)2
Now using a2 - b2 = (a + b)(a - b), we have
(p2)2 - (9)2 = (p2 + 9)(p2 -9)
We can factorise p2 - 9 further as
p2 - 9 = (p)2 - (3)2
= (p + 3)(p - 3)
∴ p4 - 81 = (p + 3)(p - 3)(p2 + 9)
Can you explain the answer of this question below:Factorise: 4y2−12y+ 9
- A:
(7y− 5)2
- B:
(5y− 3)2
- C:
(2y− 5)2
- D:
(2y− 3)2
The answer is D.
Factorise: 4y2−12y+ 9
(7y− 5)2
(5y− 3)2
(2y− 5)2
(2y− 3)2
| | Kavya Saxena answered |
We have 4y2 - 12y+9. comparing the equation with (a-b)2=a2-2ab+b2,gives us a2=(2y)2,2ab=2*3*2y and b2=(3)2.Hence the answer is (2y-3)2.
From the following, which are the factors of a2 - b + ab - a?- a)(a−1)and (a−b)
- b)(a+b)and (a−1)
- c)(a+1)and (a−b)
- d)(a+b) and (a+1)
Correct answer is option 'B'. Can you explain this answer?
From the following, which are the factors of a2 - b + ab - a?
a)
(a−1)and (a−b)
b)
(a+b)and (a−1)
c)
(a+1)and (a−b)
d)
(a+b) and (a+1)
 | Rohit Sharma answered |
a² - b + ab - a = a² + ab - b - a
= ( a² + ab ) - ( b + a )
= a ( a + b) - (a + b )
= ( a + b) ( a - 1 )
= ( a² + ab ) - ( b + a )
= a ( a + b) - (a + b )
= ( a + b) ( a - 1 )
Factorise: 10x2 − 18x3 + 14x4- a)2x2
- b)2x2(9x2−5x+7)
- c)(7x2−9x+5)
- d) 2x2(7x2−9x+5)
Correct answer is option 'D'. Can you explain this answer?
Factorise: 10x2 − 18x3 + 14x4
a)
2x2
b)
2x2(9x2−5x+7)
c)
(7x2−9x+5)
d)
2x2(7x2−9x+5)
 | Baishali Mehta answered |
10x2 − 18x3 + 14x4 = 2x(5x− 9x2 + 7x3) = 2x2(5− 9x + 7x2)
When we factorise an expression, we write it as a ________ of factors.- a)product
- b)difference
- c)sum
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
When we factorise an expression, we write it as a ________ of factors.
a)
product
b)
difference
c)
sum
d)
none of these
| | Aditya Shah answered |
When we factorise an algebraic expression, we write it as a product of factors. These factors may be numbers, algebraic variables or algebraic expressions.
Which of the following are the factors of 
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
Which of the following are the factors of
a)
b)
c)
d)
 | Riddhi Chhabra answered |
X²/4 - y²/9
Taking both in brackets of square as 2² is 4 and 3² is 9
(x/2)²-(y/3)²
now using the property (a-b)²=(a+b)(a-b)
(x/2+y/3) (x/2-y-3)
Hence the answer is option C .
Taking both in brackets of square as 2² is 4 and 3² is 9
(x/2)²-(y/3)²
now using the property (a-b)²=(a+b)(a-b)
(x/2+y/3) (x/2-y-3)
Hence the answer is option C .
What are the factors of x2+xy−2xz−2yz?- a)(x−y) and (x+2z)
- b)(x+y) and (x−2z)
- c)(x−y)and (x−2z)
- d)(x+y) and (x+2z)
Correct answer is option 'B'. Can you explain this answer?
What are the factors of x2+xy−2xz−2yz?
a)
(x−y) and (x+2z)
b)
(x+y) and (x−2z)
c)
(x−y)and (x−2z)
d)
(x+y) and (x+2z)
| | Aditya Shah answered |
x² + xy - 2xz - 2yz
x(x + y).-2z(x + y)
(x - 2z)(x + y)
Amrit and Pankaj expanded (x−5)2. Amrit's answer is x2−25 and Pankaj's answer is x2−10x+25. Which of the following statements is correct?- a)Amrit's answer is correct.
- b)Pankaj's answer is wrong.
- c)Both got correct answer.
- d)Pankaj's answer is correct.
Correct answer is option 'D'. Can you explain this answer?
Amrit and Pankaj expanded (x−5)2. Amrit's answer is x2−25 and Pankaj's answer is x2−10x+25. Which of the following statements is correct?
a)
Amrit's answer is correct.
b)
Pankaj's answer is wrong.
c)
Both got correct answer.
d)
Pankaj's answer is correct.
 | Priya Chakraborty answered |
(x−5)2 = x2−10x+25 using
(a−b)2 = a2−2ab+b2. So, Pankaj's answer is correct.
The expression (p2+7p+10) is factorized and then divided by (p+5). What is the quotient?- a)p−5
- b)p−2
- c)p+2
- d)p+5
Correct answer is option 'C'. Can you explain this answer?
The expression (p2+7p+10) is factorized and then divided by (p+5). What is the quotient?
a)
p−5
b)
p−2
c)
p+2
d)
p+5
| | Aditya Shah answered |
p^2 + 7p + 10 / p + 5
p^2 + 5p + 2p + 10 / p+5
p ( p + 5 ) + 2(p + 5 ) / p+5
( p+5) ( p+ 2 ) / p + 5
( p+2)
For x2+2x+5 to be a factor of x4+ px2+q, what must the respective values of p and q be?- a)−2 and 5
- b)5 and 25
- c)10 and 20
- d)6 and 25
Correct answer is option 'D'. Can you explain this answer?
For x2+2x+5 to be a factor of x4+ px2+q, what must the respective values of p and q be?
a)
−2 and 5
b)
5 and 25
c)
10 and 20
d)
6 and 25
 | Neha Banerjee answered |
x^4+px^2+q.
=x^2(x^2+2x+5)-2x^3–5x^2+px^2+q.
=x^2(x^2+2x+5)-2x(x^2+2x+5)+4x^2+10x-5x^2+px^2+q.
=x^2(x^2+2x+5)-2x(x^2+2x+5)+(p-1). x^2+10x+q.
=x^2(x^2+2x+5)-2x(x^2+2x+5)+(p-1)(x^2+2x+5)-2(p-1).x-5(p-1)+10x+q.
=(x^2+2x+5) (x^2–2x+p) +2(6-p).x+5(1-p)+q.
=Divisor � Q +R.
Remainder = 0
2(6-p).x+(5–5p+q)= 0.
2(6-p)x+(5–5p+q)= 0.x + 0.
Equating the coeff. of x and constant term.
2(6-p) = 0 => p = 6 and
5–5p+q = 0.
5–5�6+q = 0.
q = 30–5 = 25
p = 6 and q = 25 , Answer.
If (x2+3x+5)(x2−3x+5) = m2−n2, what is the value of m?- a)x2−3x
- b)3x
- c)x2+5
- d)x2+3x
Correct answer is option 'C'. Can you explain this answer?
If (x2+3x+5)(x2−3x+5) = m2−n2, what is the value of m?
a)
x2−3x
b)
3x
c)
x2+5
d)
x2+3x
 | Gitanjali Kaur answered |
(x2+3x+5)(x2−3x+5) = (x2+5+3x)(x2+5−3x) = (x2+5)2−(3x)2 = m2−n2
∴ m = x2+5
∴ m = x2+5
Choose the factors of 15x2−26x+8 from the following.- a)(3x−4),(5x+2)
- b)(3x−4),(5x−2)
- c)(3x+4),(5x−2)
- d)(3x+4),(5x+2)
Correct answer is option 'B'. Can you explain this answer?
Choose the factors of 15x2−26x+8 from the following.
a)
(3x−4),(5x+2)
b)
(3x−4),(5x−2)
c)
(3x+4),(5x−2)
d)
(3x+4),(5x+2)
| | Priya Chakraborty answered |
15x2−26x+8 =15x2−20x−6x+8 =5x(3x−4)−2(3x−4) =(3x−4)(5x−2)
Which of the following statements is correct?- a)(a−4)(a−2) = a2+8−6a
- b)(2p+3q)(p−q) = 2p2−3q2
- c)3p2/4p2 = 0
- d)4(m−5) = 4m−5
Correct answer is option 'A'. Can you explain this answer?
Which of the following statements is correct?
a)
(a−4)(a−2) = a2+8−6a
b)
(2p+3q)(p−q) = 2p2−3q2
c)
3p2/4p2 = 0
d)
4(m−5) = 4m−5
 | Harsh Datta answered |
(a−4)(a−2) = a2−4a−2a+8 = a2−6a+8 So, the statement in option (A) is correct.
What are the factors of x4+y4+x2y2?- a)(x2+y2) and (x2+y2−xy)
- b)(x2+y2)and (x2−y2)
- c)(x2+y2+xy) and (x2+y2−xy)
- d)Factorization is not possibl
Correct answer is option 'C'. Can you explain this answer?
What are the factors of x4+y4+x2y2?
a)
(x2+y2) and (x2+y2−xy)
b)
(x2+y2)and (x2−y2)
c)
(x2+y2+xy) and (x2+y2−xy)
d)
Factorization is not possibl
 | Gargi Shah answered |
x4+y4+x2y2 =(x4+y4+2x2y2)−x2y2 =(x2+y2)2−(xy)2
=(x2+y2+xy)(x2+y2−xy)
=(x2+y2+xy)(x2+y2−xy)
Divide the given polynomial by the given monominal: 8 (x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2- a)(x + y + z)
- b)2(x + y + z)
- c)2
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Divide the given polynomial by the given monominal: 8 (x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2
a)
(x + y + z)
b)
2(x + y + z)
c)
2
d)
none of these
| | Nitin Sen answered |
To divide a polynomial by a monomial, we need to divide each term in the polynomial by the monomial.
Given polynomial: 8x^3y^2z^2 - x^2y^3z^2 - x^2y^2z^3
Given monomial: 8
Dividing each term by the monomial 8:
(8x^3y^2z^2)/8 = x^3y^2z^2
(-x^2y^3z^2)/8 = -1/8 * x^2y^3z^2
(-x^2y^2z^3)/8 = -1/8 * x^2y^2z^3
Therefore, the result of dividing the given polynomial by the monomial 8 is:
x^3y^2z^2 - (1/8)x^2y^3z^2 - (1/8)x^2y^2z^3
Given polynomial: 8x^3y^2z^2 - x^2y^3z^2 - x^2y^2z^3
Given monomial: 8
Dividing each term by the monomial 8:
(8x^3y^2z^2)/8 = x^3y^2z^2
(-x^2y^3z^2)/8 = -1/8 * x^2y^3z^2
(-x^2y^2z^3)/8 = -1/8 * x^2y^2z^3
Therefore, the result of dividing the given polynomial by the monomial 8 is:
x^3y^2z^2 - (1/8)x^2y^3z^2 - (1/8)x^2y^2z^3
Find the factors of6 mn−4n+6−9m.- a)(2m−1) and (2n−4)
- b)(4m−1) and (n−3)
- c)(3m−2) and (2n−3)
- d)(4m−4) and (n−1)
Correct answer is option 'C'. Can you explain this answer?
Find the factors of6 mn−4n+6−9m.
a)
(2m−1) and (2n−4)
b)
(4m−1) and (n−3)
c)
(3m−2) and (2n−3)
d)
(4m−4) and (n−1)
| | Aditya Shah answered |
6mn-9m-4n+6
take 3m common
3m(2n-3)-2(2n-3)
(3m-2)(2n-3)
Which of the following is one of the factors of x4+4?- a)x2+2
- b)(x² + 2 + 2x)(x² + 2 - 2x)
- c)x2−2
- d)x2+2x−2
Correct answer is option 'B'. Can you explain this answer?
Which of the following is one of the factors of x4+4?
a)
x2+2
b)
(x² + 2 + 2x)(x² + 2 - 2x)
c)
x2−2
d)
x2+2x−2
 | Amrutha Saini answered |
x4+4
adding and subtracting 4x2
x4+4+4x2−4x2
(x2)2+22+2∗2∗x2−(2x)2
(x2+2)2−(2x)2(a+b)2=a2+b2+2ab
(x2+2−2x)(x2+2+2x)(a2−b2)=(a+b)(a−b)
Find the factors of b2−7b+12.- a)(b−4),(b−8)
- b)(b−3),(b−4)
- c)(b−10),(b−1)
- d)(b−7),(b−9)
Correct answer is option 'B'. Can you explain this answer?
Find the factors of b2−7b+12.
a)
(b−4),(b−8)
b)
(b−3),(b−4)
c)
(b−10),(b−1)
d)
(b−7),(b−9)
 | Saanvi Joshi answered |
b2 - 7b+12=b2-3b-4b+12=b(b-3)-4(b-3)=(b-3)(b-4)
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