Mathematics

When a polynomial is divided by a linear factor like $x+1$, the Remainder Theorem tells us that the remainder equals the polynomial evaluated at the root of that divisor. Here, $x+1=0$ means $x=-1$, so you just need to plug $-1$ into $q(x)$ and set it equal to the given remainder of $-2$. This turns a division problem into a simple equation to solve for $a$.

When a polynomial is divided by a linear factor like $x+1$, the Remainder Theorem tells us that the remainder equals the polynomial evaluated at the root of that divisor. Here, $x+1=0$ means $x=-1$, so you just need to plug $-1$ into $q(x)$ and set it equal to the given remainder of $-2$. This turns a division problem into a simple equation to solve for $a$.