The Factor Theorem states that a polynomial f(x) has a factor (x-c) if and only if f(c) = 0.

In this case, we are asked to determine if (x + 3) is a factor of the polynomial f(x) = x^4 + 8x^3 + 11x^2 - 11x + 3.

To do this, we need to substitute x = -3 into the polynomial and see if it equals zero.

f(-3) = (-3)^4 + 8(-3)^3 + 11(-3)^2 - 11(-3) + 3
= 81 - 216 + 99 + 33 + 3
= 0

Since f(-3) = 0, by the Factor Theorem, (x + 3) is a factor of the polynomial f(x) = x^4 + 8x^3 + 11x^2 - 11x + 3.

So, the answer is b. Yes.

Question

The Factor Theorem states that a polynomial f(x) has a factor (x-c) if and only if f(c) = 0.

In this case, we are asked to determine if (x + 3) is a factor of the polynomial f(x) = x^4 + 8x^3 + 11x^2 - 11x + 3.

To do this, we need to substitute x = -3 into the polynomial and see if it equals zero.

f(-3) = (-3)^4 + 8(-3)^3 + 11(-3)^2 - 11(-3) + 3
       = 81 - 216 + 99 + 33 + 3
       = 0

Since f(-3) = 0, by the Factor Theorem, (x + 3) is a factor of the polynomial f(x) = x^4 + 8x^3 + 11x^2 - 11x + 3.

So, the answer is b. Yes.

Knowee AI · Accepted Answer

The Factor Theorem states that a polynomial f(x) has a factor (x-c) if and only if f(c) = 0.

In this case, we are asked to determine if (x + 3) is a factor of the polynomial f(x) = x^4 + 8x^3 + 11x^2 - 11x + 3.

To do this, we need to substitute x = -3 into the polynomial and see if it equals zero.

f(-3) = (-3)^4 + 8(-3)^3 + 11(-3)^2 - 11(-3) + 3
       = 81 - 216 + 99 + 33 + 3
       = 0

Since f(-3) = 0, by the Factor Theorem, (x + 3) is a factor of the polynomial f(x) = x^4 + 8x^3 + 11x^2 - 11x + 3.

So, the answer is b. Yes.

Use the factor theorem to determine if the given binomial is a factor of f (x).f (x) = x4 + 8x3 + 11x2 - 11x + 3; x + 3Select one:a. Nob. Yes