Advertisements
Advertisements
प्रश्न
Factorize the following polynomial.
(x – 3) (x – 4)2 (x – 5) – 6
Advertisements
उत्तर
(x – 3) (x – 4)2 (x – 5) – 6
= (x – 3)(x – 5) (x – 4)2 – 6
= (x2 – 8x + 15) (x2 – 8x + 16) – 6
Let x2 – 8x = z
∴ (x2 − 8x + 15) (x2 − 8x + 16) − 6
= (z + 15) (z + 16) − 6
= z2 + 31z + 240 − 6
= z2 + 31z + 234
= z2 + 18z + 13z + 234
= z(z + 18) 13(z + 18)
= (z + 18) (z + 13)
= (x2 − 8x + 18) (x2 − 8x + 13) ...(Replace z = x2 − 8x)
APPEARS IN
संबंधित प्रश्न
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
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = x2 + x + k
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = `kx^2 - sqrt2x +1`
Factorise:
x3 – 2x2 – x + 2
Factorise:
x3 – 3x2 – 9x – 5
Determine the following polynomial has (x + 1) a factor:
x4 + x3 + x2 + x + 1
Determine the following polynomial has (x + 1) a factor:
`x^3-x^2-(2+sqrt2)x+sqrt2`
Find the factor of the polynomial given below.
2m2 + 5m – 3
Find the factor of the polynomial given below.
12x2 + 61x + 77
Factorize the following polynomial.
(x2 – 2x + 3) (x2 – 2x + 5) – 35
Factorize the following polynomial.
(y2 + 5y) (y2 + 5y – 2) – 24
If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is ______.
One of the factors of (25x2 – 1) + (1 + 5x)2 is ______.
The factorisation of 4x2 + 8x + 3 is ______.
Determine which of the following polynomials has x – 2 a factor:
3x2 + 6x – 24
Factorise:
1 + 64x3
Find the following product:
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
Factorise:
`2sqrt(2)a^3 + 8b^3 - 27c^3 + 18sqrt(2)abc`
Without finding the cubes, factorise:
(x – 2y)3 + (2y – 3z)3 + (3z – x)3
