Question

Is x + 9 a factor of the polynomial P(x) = x^3 + 11x^2 + 15x -27? If so, write the polynomial as a product of two factors. If not, explain how you know.

Answer 1

The factors of polynomial are (x-1) and (x+3)

Step-by-step explanation:

If (x+9) is a factor of P(x)= x³+11x²+15x-27 then the P(x) must be completely divisible by (x+9)

After finding the polynomial, we need to factorise the polynomial by utilising the quadratic equation.

All the process has been described in image attached-

S₁, S₂, S₃ represents various steps involved in solving the problem.

It is found that (x+9) is a factor of   x³+11x²+15x-27

The polynomial found after dividing   x³+11x²+15x-27 by (x+9) is  x²+2x-3

Which can be further factorised by quadratic rule into the factors as (x-1) and (x+3)

Hence the factors are (x-1) and (x+3)