Advertisements
Advertisements
प्रश्न
Factorize the following polynomial.
(y + 2) (y – 3) (y + 8) (y + 3) + 56
Advertisements
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
Determine the following polynomial has (x + 1) a factor:
x3 + x2 + 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
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = `2x^2+kx+sqrt2`
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = `kx^2 - sqrt2x +1`
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = kx2 – 3x + k
Factorise:
6x2 + 5x – 6
Factorise:
x3 – 3x2 – 9x – 5
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
The factorisation of 4x2 + 8x + 3 is ______.
Show that p – 1 is a factor of p10 – 1 and also of p11 – 1.
Find the value of m so that 2x – 1 be a factor of 8x4 + 4x3 – 16x2 + 10x + m.
Factorise:
6x2 + 7x – 3
Factorise:
2x2 – 7x – 15
Factorise:
84 – 2r – 2r2
Factorise the following:
9x2 – 12x + 3
Factorise:
a3 – 8b3 – 64c3 – 24abc
Factorise:
`2sqrt(2)a^3 + 8b^3 - 27c^3 + 18sqrt(2)abc`
