Question

Factorise x3 + 13 x2 + 32x + 20

Answer 1

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

= x^3 + x^2 + 12x^2 + 12x + 20x + 20

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

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

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

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

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

Answer 2

Hi pupil here's your answer ::

______________________________

To factorise a cubic term,
First 》 find the factors of the last digit that is 20 so they can be 1 2 4 5 10 20

Second 》first take -1 as the sign in the term is positive

Third 》check by remainder theorem
-1^3 + 13(-1)^2 + 32×(-1) +20

-1 + 13 - 32 +20

0

so , x=-1 ⏩x+1=0

now divide it

$\frac{{x}^{3} + {13x}^{2} + 32x + 20 }{x + 1}$

so the factors coming by dividing are

⏩x2 + 12x + 20 factorise it
⏩x2 +2x + 10y + 20
⏩x (x+2) + 10 (x+2)
⏩(x+2) (x+10)

so now these are two factors and another one that we have found in starting write them

(x+1) (x+2) ⚫ (x+10)


_____________________________

hope that it helps. . . . . . . .