Question

Determine whether the binomial (x+4) is a factor of the polynomial p(x) = 3x^3 - x^2 - 62x - 40.

(True/False)

Answer 1

To determine whether (x+4) is a factor of p(x), substitute -4 into the polynomial and see if it equals zero.

Step-by-step explanation:

To determine whether the binomial (x+4) is a factor of the polynomial p(x) = 3x^3 - x^2 - 62x - 40, you can use the Remainder Theorem. Substitute -4 into the polynomial to see if it equals zero. If it does, then (x+4) is a factor of the polynomial. In this case, substituting -4 into the polynomial gives:

p(-4) = 3(-4)^3 - (-4)^2 - 62(-4) - 40 = 0

Since the result is zero, we can conclude that (x+4) is a factor of the polynomial.