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) = kx2 – 3x + k
Factorise:
12x2 – 7x + 1
Factorise:
x3 – 3x2 – 9x – 5
Factorise:
x3 + 13x2 + 32x + 20
Find the Factors of the Polynomial Given Below.
2x2 + x – 1
Find the factor of the polynomial given below.
12x2 + 61x + 77
Factorize the following polynomial.
(y2 + 5y) (y2 + 5y – 2) – 24
The factorisation of 4x2 + 8x + 3 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
Show that p – 1 is a factor of p10 – 1 and also of p11 – 1.
If x + 1 is a factor of ax3 + x2 – 2x + 4a – 9, find the value of a.
Factorise:
x2 + 9x + 18
Factorise:
1 + 64x3
