Question

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

Answer 1

`(x+3)` is not a factor of the expression

Explanation:

By the Factor Theorem, if `(x+3)` is a factor of the expression then `x=-3` will be a zero of the expression. We can test this by substituting `x=-3` into the expression.
`2(-3)^4 +5(-3)^3 -2(-3)^2 +5(-3) +(-3)`
`=162-135-18-15-3`
`=-9 != 0`

Therefore `(x+3)` is not a factor of the expression.