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 x4+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 x4+2x2+9?
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)
For x2+2x+5 to be a factor of x4+ px2+q, what must the respective values of p and q be?
Let the other factor be x2+ax+b. We have (x2+2x+5)(x2+ax+b)
x4(2+a)x3(2a+b+5)x2(5a+2b)x+5b = x4+px2+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 x2+xy−2xz−2yz?
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?
(x−5)2 = x2−10x+25 using
(a−b)2 = a2−2ab+b2. So, Pankaj's answer is correct.
Find the quotient when 5a2b2c2 is divided by 15abc.
Which of the following statements is correct?
(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?
x4+y4+x2y2 =(x4+y4+2x2y2)−x2y2 =(x2+y2)2−(xy)2
Choose the factors of 15x2−26x+8 from the following.
15x2−26x+8 =15x2−20x−6x+8 =5x(3x−4)−2(3x−4) =(3x−4)(5x−2)
How many factors does (x9−x) have?
Which of the following are the factors of
What is the coefficient of 'a' when 9a2+18a is divided by (a+2)?
From the following, which are the factors of a2+b−ab−a?
The expression (p2+7p+10) is factorized and then divided by (p+5). What is the quotient?
Which is the correct statement in the following?
n(3n+2) = 3n2+2n
If (x2+3x+5)(x2−3x+5) = m2−n2, what is the value of m?
(x2+3x+5)(x2−3x+5) = (x2+5+3x)(x2+5−3x) = (x2+5)2−(3x)2 = m2−n2
∴ m = x2+5
Divide 6p5+18p4−3p2 by 3p2.
Find the factors of b2−7b+12.
b2 - 7b+12=b2-3b-4b+12=b(b-3)-4(b-3)=(b-3)(b-4)
Find the factors of6 mn−4n+6−9m.