Question

Factrise x^3+6x^2+5x_12 and verify by the product of factors

Answer 1

Answer:

(x+3)(x+4)(x–1)

Step-by-step explanation:

factorising x³+6x²+5x–12=p(x)

As it is cubic polynomial first check 1

when x=1

1+6+5–12=0

it is true so x–1 is factor p(x)

when p(x) is divided by x–1 quotient=x²+7x+12=q(x

when we factorise q(x)

x²+3x+4x+12

x(x+3)+4(x+3)

(x+3)(x+4)

we get (x+3)and(x+4)

thus;(x+3)(x+4)(x–1) are factors of p(x)

VERIFICATION

(x+3)(x+4)(x–1)

x³+x²(3+4–1)+x(12–3–4)+(–12)

x³+6x²+5x–12