Question

How do you use the factor theorem to determine whether v+5 is a factor of `v^4 + 16v^3 + 8v^2 - 725`?

Answer 1

To find if v+5 is a factor then plug in v=-5 in the given polynomial, if the result obtained is zero, then it is a factor.

Explanation:

If `x-a` is a factor of the polynomial `P(x)` then by factor theorem `P(a)=0`.

Our question we have to check if `v+5` is a factor of `v^4+16v^3+8v^2-725`

`(-5)^4 + 16(-5)^3 + 8(-5)^2 - 725`

`=625 -2000 + 200 - 725`

`=-1900`

`We infer that v+5 is not a factor.`