Answer:
9
Step-by-step explanation:
This is a straightforward application of the Remainder Theorem, which states that any polynomial [tex]p(x)[/tex] , when divided by a linear factor [tex](x-a)[/tex] will have a remainder equal to evaluating the function [tex]p(x)[/tex] at [tex]x=a[/tex]
To find the remainder of [tex]x^{3}-4x^{2}-12x+9[/tex] when divided by [tex](x+2)[/tex] , we have to evaluate the polynomial at [tex]x=-2[/tex]
Let's do it.
[tex](-2)^{3}-4(-2)^{2}-12(-2)+9\\=9[/tex]
Hence, 9 is the remainder.
