Find the quotient when two 𝑥 cubed plus seven 𝑥 squared minus eight 𝑥 minus 21 is divided by two 𝑥 plus three.
Our first step is to determine what we multiply two 𝑥 by in order for it to look like two 𝑥 cubed. We would have to multiply by 𝑥 squared, so let’s put that above the 𝑥 squared term; and now we distribute.
When we subtract, we get four 𝑥 squared. And now we start the process over: what do we multiply two 𝑥 by so it’s equal to four 𝑥 squared? That would be two 𝑥, and we put it above the 𝑥 term. Distribute, and now we will have to bring down the negative eight 𝑥.
And now we subtract and we get negative 14𝑥. So what do we multiply two 𝑥 by so it’s equal to negative 14𝑥?
That would be negative seven. Distribute, and bring down the negative 21, and now subtract, and we get zero.
That means there’s no remainder so, our final answer is 𝑥 squared plus two 𝑥 minus seven.