Question

Create your own third degree polynomial that when divided by x + 2 has a remainder of –4.

Answer 1

Think about what happens when you divide something by x+2: you get a quotient Q, and a remainder R. You can write that as Q+R/(x+2). In the case where R=-4, you get Q+(-4)/(x+2). So, pick any Q you want, multiply it all by x+2, and you'll get a polynomial that has a remainder of -4 when divided by x+2. But you need a third degree polynomial. So think about what happens when you divide a third-degree polynomial by x+2: you get a second-degree polynomial, plus a remainder. So choose Q to be quadratic, and you'll get a viable answer.