Question

Need Help with some Math

Determine the remainder when f(x) = 3x^15 - 5x^12 + 7x^6 - 3x^2 + 12 is divided by x + 1

Answer 1

8

Explanation:

We can use the Polynomial Remainder Theorem. The PRT states that if we have a polynomial
`f(x)` being divided by a factor in the form of
`(x-a)`, then the remainder of the polynomial is given by
`f(a)`.

We have the polynomial:

`f(x)=3x^(15)-5x^(12)+7x^6-3x^2+12`

And it is being divided by:

`(x+1)`

We can rewrite our factor as:

`(x-(-1))`

Therefore:

`a=-1`

Then our remainder will be:

`f(-1)`

Evaluate:

`\begin{aligned} f(-1)&=3(-1)^(15)-5(-1)^(12)+7(-1)^6-3(-1)^2+12\\&=-3-5+7-3+12\\&=8 \end{aligned}`

So, our remainder will be 8.