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