Question

factorise x cube + 13 x square + 32 X + 20​

Answer 1

x^3+13x^2+32x+20

Let x=-1

p(x)=x^3+13x^2+32x+20

p(-1)=(-1)^3+13(-1)^2+32(-1)+20

=-1+13(1)+(-32)+20

=-1+13-32+20

=12-12

p(-1)=0

1st factor=(x+1)

(x^3+13x^2+32x+20)÷(x+1)

=x^2+12x+20

Then,

(x+1)(x^2+12x+20)

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

=(x+1)[(x^2+10x)+(2x+20)]

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

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

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