Consider the rational expression (4x^2-7x+16)/(x+1). What is the remainder when the expression is read as a division problem?

Question

Consider the rational expression
`(4x^2-7x+16)/(x+1)`.

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

Answer 1

Remainder = 27

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).