What are the factors of ax+by+bx+az+ay+bz?
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)
Which of the following is one of the factors of x^{4}+4?
x⁴ + 4
= (x² + 2)²  4x²
= (x² + 2)²  (2x)²
a²  b² = (a + b)(a  b)
= (x² + 2 + 2x)(x² + 2  2x)
What are the factors of x^{4}+2x^{2}+9?
Given equation is x^{4} + 2x^{2} + 9
We can rewrite this as,
(x^{2})^{2} + 6x^{2} + 9 − 4x^{2}
⇒ (x^{2} + 3)^{2} − (2x)^{2}
....Since a^{2} + 2ab + b^{2} = (a+b)^{2}
⇒ x^{4} + 2x^{2} + 9 = (x^{2} − 2x + 3)(x^{2} + 2x + 3)
....Since a^{2 }− b^{2} = (a+b)(a−b)
For x^{2}+2x+5 to be a factor of x^{4}+ px^{2}+q, what must the respective values of p and q be?
Let the other factor be x^{2}+ax+b. We have (x^{2}+2x+5)(x^{2}+ax+b)
= x^{4}+px^{2}+q
x^{4}(2+a)x^{3}(2a+b+5)x^{2}(5a+2b)x+5b = x4+px^{2}+q
Comparing the coefficients of corresponding terms, we get 2a+b+5 = p ......(1)
5b = q ......(2)
2+a = 0 ⇒ a =−2
5a+2b = 0 ⇒ b = 5
∴ p = 2a+b+5 = 2(−2)+5+5 = 6
q = 5b = 5(5) = 25
What are the factors of x^{2}+xy−2xz−2yz?
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 x^{2}−25 and Pankaj's answer is x^{2}−10x+25. Which of the following statements is correct?
(x−5)^{2} = x^{2}−10x+25 using
(a−b)^{2} = a^{2}−2ab+b^{2}. So, Pankaj's answer is correct.
Find the quotient when 5a^{2}b^{2}c^{2} is divided by 15abc.
Which of the following statements is correct?
(a−4)(a−2) = a^{2}−4a−2a+8 = a^{2}−6a+8 So, the statement in option (A) is correct.
What are the factors of x^{4}+y^{4}+x^{2}y^{2}?
x^{4}+y^{4}+x^{2}y^{2} =(x^{4}+y^{4}+2x^{2}y^{2})−x^{2}y^{2} =(x^{2}+y^{2})^{2}−(xy)^{2}
=(x^{2}+y^{2}+xy)(x^{2}+y^{2}−xy)
Choose the factors of 15x^{2}−26x+8 from the following.
15x^{2}−26x+8 =15x^{2}−20x−6x+8 =5x(3x−4)−2(3x−4) =(3x−4)(5x−2)
How many factors does (x^{9}−x) have?
f(x)=x9−x
=x(x8−1)
=x[(x4)2−(1)2]
=x[(x4−1)(x4+1)]
=x(x4+1)[(x2)2−12]
=x(x4+1)(x2+1)(x2−1)
=x(x4+1)(x2+1)(x−1)(x+1)
∴ There are 5 factors of f(x)⇒(x),(x4+1),(x2+1),(x−1) and (x+1)
Which of the following are the factors of
What is the coefficient of 'a' when 9a^{2}+18a is divided by (a+2)?
From the following, which are the factors of a^{2 } b + ab  a?
a²  b + ab  a = a² + ab  b  a
= ( a² + ab )  ( b + a )
= a ( a + b)  (a + b )
= ( a + b) ( a  1 )
The expression (p^{2}+7p+10) is factorized and then divided by (p+5). What is the quotient?
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)
Which is the correct statement in the following?
n(3n+2) = 3n^{2}+2n
If (x^{2}+3x+5)(x^{2}−3x+5) = m^{2}−n^{2}, what is the value of m?
(x^{2}+3x+5)(x^{2}−3x+5) = (x^{2}+5+3x)(x^{2}+5−3x) = (x^{2}+5)^{2}−(3x)^{2 }= m^{2}−n^{2}
∴ m = x^{2}+5
Divide 6p^{5}+18p^{4}−3p^{2} by 3p^{2}.
Find the factors of b^{2}−7b+12.
b^{2 } 7b+12=b^{2}3b4b+12=b(b3)4(b3)=(b3)(b4)
Find the factors of6 mn−4n+6−9m.
6mn9m4n+6
take 3m common
3m(2n3)2(2n3)
(3m2)(2n3)
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 








