The polynomial's factors 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)
