Question

How do you use the remainder theorem to see if the `p+5` is a factor of `p^4+6p^3+11p^2+29p-13`?

Answer 1

Not a factor.

Explanation:

Before even using the remainder theorem, you can see that `(p+5)` will not be a factor because the expression ends with `-13` which is not divisible by 5.

But looking at it again using the remainder theorem...

Call The expression `f(p)`

`f(p) = p^4 +6p^3+11p^2+29p-13`

If `p+5 = 0 rarr p = -5`

Calculate `f(-5)` by substituting (-5) for every `p`

If the answer is equal to `0`, it means that `(p+5)` is a factor.

If the answer is not `0`, then the value you get will be the remainder if you divide by `(p+5)`

`f(p) = p^4 +6p^3+11p^2+29p-13`

`f(-5) = (-5)^4 +6(-5)^3+11(-5)^2+29(-5)-13`

`=625-750+275-145 -13`

`=-8`

Nope, not a factor!