Advertisements
Advertisements
Question
Factorize the following polynomial.
(x – 5)2 – (5x – 25) – 24
Advertisements
Solution
(x – 5)2 – (5x – 25) – 24
= (x – 5)2 – 5(x – 5) – 24
Let x – 5 = z
∴ (x – 5)2 – 5 (x – 5) – 24
= z2 – 5z – 24
= z2 – 8z + 3z – 24
= z (z – 8) + 3 (z – 8)
= (z – 8) (z + 3)
= (x – 5 – 8) (x – 5 + 3) (Replace z = x - 5)
= (x – 13) (x – 2)
APPEARS IN
RELATED QUESTIONS
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:
p(x) = 2x3 + x2 – 2x – 1, g(x) = x + 1
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:
p(x) = x3 − 4x2 + x + 6, g(x) = x − 3
Factorise:
12x2 – 7x + 1
Factorise:
3x2 – x – 4
Factorise:
2y3 + y2 – 2y – 1
Determine the following polynomial has (x + 1) a factor:
x4 + x3 + x2 + x + 1
Find the factor of the polynomial given below.
2m2 + 5m – 3
Find the factor of the polynomial given below.
12x2 + 61x + 77
Find the factor of the polynomial given below.
`1/2x^2 - 3x + 4`
Factorize the following polynomial.
(x2 – x)2 – 8 (x2 – x) + 12
Factorize the following polynomial.
(x2 – 2x + 3) (x2 – 2x + 5) – 35
Factorize the following polynomial.
(y2 + 5y) (y2 + 5y – 2) – 24
Factorize the following polynomial.
(x – 3) (x – 4)2 (x – 5) – 6
Which of the following is a factor of (x + y)3 – (x3 + y3)?
Factorise:
2x2 – 7x – 15
Factorise:
1 + 64x3
Factorise:
a3 – 8b3 – 64c3 – 24abc
Without finding the cubes, factorise:
(x – 2y)3 + (2y – 3z)3 + (3z – x)3
