Question

Factorise the following by factor theorem: x^3+9x^2+23x+15

Answer 1

Step-by-step explanation:

let the polynomial be f(x)

now f(-1) =0

=>x+1 is a factor of f(x)

taking x+1 as common

f(x) =x^3+x²+8x²+8x+15x+15

=(x+1)(x²+8x+15)

=(x+1)(x+3)(x+5)

Answer 2

Answer:

(x+1)(x+8x+15)

Step-by-step explanation:

put -1 in place of x

p(-1)=(-1)^3+9×1+23×1+15

p(-1)=0

then one factor is x=-1

x+1=0

p(x)=x^3+x^2+8x^2+8x+15x+15

=x^2(x+1)+8x(x+1)+15(x+1)

=(x^2+8x+15)(x+1)