Answer:
Yes, it is a factor.
[tex]p(x) = (x + 9)( {x}^{2} + 2x - 3)[/tex]
Step-by-step explanation:
Let us quickly perform a synthetic synthetic division to determine whether x+9 is a factor of
[tex]p(x) = {x}^{3} + 11 {x}^{2} + 15x - 27[/tex]
We perform the synthetic division as shown in attachment.
Since the remainder is zero, x+9 is a factor of p(x).
From the results of our division, the quotient is :
[tex]q(x) = {x}^{2} + 2x - 3[/tex]
Therefore the polynomial as a product of two factors is:
[tex]p(x) = {x}^{3} + 11 {x}^{2} + 15x - 27 = (x + 9)( {x}^{2} + 2x - 3)[/tex]
