Use the Remainder Theorem to determine if x - 2 is a factor of the polynomial: f(x) = 3x^5 - 7x^3 - 11x^2 + 2

I am confused because I cannot rationally factor this polynomial. Does it want me to use x - 2 as a denominator?

Oh sorry, I got it. Go ahead and delete this post:/

To determine if x - 2 is a factor of the polynomial f(x) = 3x^5 - 7x^3 - 11x^2 + 2, you can use the Remainder Theorem.

The Remainder Theorem states that if a polynomial f(x) is divided by x - a, then the remainder will be f(a). So, if x - 2 is a factor of f(x), then f(2) should be equal to 0.

To use the Remainder Theorem, substitute x = 2 into the polynomial and evaluate the expression.

f(2) = 3(2)^5 - 7(2)^3 - 11(2)^2 + 2
= 3(32) - 7(8) - 11(4) + 2
= 96 - 56 - 44 + 2
= -2

Since f(2) = -2 and not 0, we can conclude that x - 2 is not a factor of the polynomial f(x) = 3x^5 - 7x^3 - 11x^2 + 2.

It's important to note that factoring the polynomial will not give you the answer in this case. The Remainder Theorem is a more efficient method to determine if a given binomial is a factor of a polynomial.