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Factorise each of the following polynomials …

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Factorise each of the following polynomials , given that : X ^3 + 13x^2 + 32 x + 20 , (X + 2 ) is a factor .

Posted by Ashutosh Kashyap 5 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 5 months ago

Let p(x) = x³ + 13x²+ 32x + 20
p(-1) = (-1)³ + 13(-1)² + 32(-1) + 20
= -1 + 13 - 32 + 20 = 0
∴ By Factor Theorem, x - (-1), i.e., (x + 1) is a factor of p(x).
x³ + 13x² + 32x + 20
= x²(x + 1) + 12x(x + 1) + 20(x + 1)
= (x + 1)(x² + 12x + 20)
= (x + 1)(x² + 2x + 10x + 20)
= (x + 1){x(x + 2) + 10(x + 2)}
= (x + 1)(x + 2)(x + 10).

1Thank You

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CBSE > Class 09 > Mathematics