Question

What is the remainder when 4x^3+8x-32 is divided by x+10?

Answer 1

The remainder is -4112.

Explanation:

We can use the Polynomial Remainder Theorem. According to the PRT, when we divide a polynomial P(x) by a binomial in the form of (x - a), then the remainder will be P(a).

We are dividing:

`(4x^3+8x-32)\text{ by } (x+10)`

We can rewrite the divisor as:

`x+10=x-(-10)`

So, a = -10.

Then according to the PRT, the remainder of the operation will be:

`R=P(-10)=4(-10)^3+8(-10)-32=-4112`