Finding the value of $A$ and $B$

Question

The polynomial $f(x) = A(x-1)^2 + B(x+2)^2$ is divided by $x + 1$ and $x - 2$. The remainders are $3$ and $-15$ respectively,

I don't really know how to begin this with, help me with the steps

Answer 1

Remainder theorem states that the remainder of the division of a polynomial $f(x)$ by a linear polynomial $(x-r)$ is equal to $f(r)$.

So,$f(-1)=4A+B=3$ and $f(2)=A+16B=-15$.

Two equations and two variables, now its upon you!

Answer 2

The remainder of $$f(x) = A(x-1)^2 + B(x+2)^2$$ in dividing by $x-c$ is $f(c)$

Therefore you have $$f(-1)=3$$ and $$f(2)=-15$$

That results in $$4A+B=3$$ and $$A+16B=-15$$

Solve for $A$ and $B$ to find your answer.