Is (x-4) a factor of 2x^4-9x^3-20x^2+147x-180? find out by using the factor theorem.

(x-4) is not a factor of the given polynomial.

Explanation:

Rule: If (x-k) is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem. We can take this in reverse to say that if p(k) = 0, then (x-k) must be a factor of p(x).

In this case, we have k = 4 and we can find that:

p(x) = 2x^4-9x^3-20x^2+147x-180

p(4) = 2(4)^4-9(4)^3-20(4)^2+147(4)-180

p(4) = 24

The result we get is not zero, so that means (x-4) is not a factor of p(x).