Question

Consider the rational expression $\frac{4x^2-7x+16}{x+1}$.

What is the remainder when the expression is read as a division problem?

Answer 1

Answer:

Remainder = 27

Step-by-step explanation:

We can use the Remainder Theorem here. This says that  the remainder when f(x) is divided by x - a is f(a).

So here f(-1) will give us the remainder:-

f(-1) = 4(-1)^2 - 7(-1) + 16

= 4 + 7 + 16

= 27

If we did the long division we'd get the alternative form

4x - 11 + 27/(x + 1).