Question

Which of the following is a factor of p x x 2 − 4x − 5?(x+5)(x - 1)(x+5)(x + 1)(x + 1)(x - 5)(x - 1)(x - 5)

Answer 1

(x+5)(x - 1) is a factor of p(x) = x² - 4x - 5

We can see that by applying polynomial long division or by applying synthetic division, both of these methods will give the same result.

x² - 4x - 5 = (x + 5)(x - 1)q(x) + r(x)

where q(x) and r(x) are the quotient and remainder of the polynomial division respectively. Since r(x) = 0, it means (x + 5)(x - 1) is a factor of p(x) = x² - 4x - 5.