Question

$x {}^{2} + 13x {}^{2} + 32x + 20 \: factorise$
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Answer 1

Let p(x) = x3 + 13x2 + 32x + 20

p(-1) = -1 + 13 - 32 + 20 = -33 + 33 = 0

Therefore (x + 1) is a factor of p(x).

On dividing p(x) by (x + 1) we get

p(x) (x + 1) = x2 + 12x + 20

Thus,

x3 + 13x2 + 32x + 20 = (x + 1)(x2 + 12x + 20)

= (x + 1) (x2 + 10x + 2x + 20)

= (x + 1)[x(x + 10) + 2(x + 10)]

= (x + 1) (x +2) (x + 10)

Hence, x3 + 13x2 + 32x + 20 = (x + 1) (x +2) (x + 10).