Question

x^3+15x^2+32x+20 factorise​

Answer 1

Answer:

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)

Step-by-step explanation:

Factor theorem is used here

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

start by sub x= 1,-1,.... to get p(x)=0

now

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

so x+1 is a factor......factor theorem

now divide x3 + 13x2 + 32x + 20 by x+1......long division

you will get remainder zero, and quotient =x2 + 12x + 20

so,

Divident =divisor x quotient +remainder

x3 + 13x2 + 32x + 20 = (x + 1)(x2 + 12x + 20)......factorize x2 + 12x + 20 by spliting middle term