Question

Use the factor theorem to determine if the given binomial is a factor of f (x).

f(x) = x4 + 8x3 + 11x2 -11x + 3; (x + 3)

Answer 1

The binomial is a factor

Explanation:

In order to show that x+3 is a factor of the polynomial, then;

f(a) = 0

Get a by equating x+3 to zero

x+3 = 0

x = -3

Get f(-3)

f(-3) = (-3)^4 + 8(-3)^3 + 11(-3)^2 -11(-3) + 3

f(-3) = 81 - 216 + 99 + 33 + 3

f(-3) = 216-216

f(-3) = 0

Since the remainder of the polynomial when divided by x+3 is zero, this shows that x+3 is a factor of the given polynomial