Advertisements
Advertisements
प्रश्न
Factorize the following polynomial.
(y + 2) (y – 3) (y + 8) (y + 3) + 56
उत्तर
(y + 2) (y – 3) (y + 8) (y + 3) + 56
= (y + 2) (y + 3) (y + 8) (y – 3) + 56
= (y2 + 3y + 2y + 6) (y2 + 8y - 3y - 24) + 56
= (y2 + 5y + 6) (y2 + 5y – 24) + 56
Let y2 + 5y = z
∴ (y2 + 5y + 6) (y2 + 5y - 24) + 56
= (z + 6 ) (z - 24) + 56
= z2 - 24z + 6z - 144 + 56
= z2 - 18z - 144 + 56
= z2 - 18z - 88
= z2 - 22z + 4z - 88
= z (z - 22) + 4 (z - 22)
= (z - 22) (z + 4)
= (y2 + 5y - 22) (y2 + 5y + 4) ...(Replace z = y2 + 5y)
= (y2 + 5y - 22) (y2 + 4y + y + 4)
= (y2 + 5y - 22) [y (y + 4) + 1 ( y + 4)]
= (y2 + 5y - 22) (y + 4) (y + 1)
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) = 2x3 + x2 – 2x – 1, g(x) = x + 1
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:
6x2 + 5x – 6
Factorise:
x3 + 13x2 + 32x + 20
Factorize the following polynomial.
(x2 – 2x + 3) (x2 – 2x + 5) – 35
If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is ______.
Show that 2x – 3 is a factor of x + 2x3 – 9x2 + 12.
Determine which of the following polynomials has x – 2 a factor:
3x2 + 6x – 24
Factorise:
2x2 – 7x – 15
Find the following product:
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
