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

Question

I feel like I went too far or messed up please help

The binomial (x-2) is not a factor because the remainder does not equal 0 when factored out, it equals -2. I missed this because i used the line method and messed up my values, after looking at the live lesson i learned how to factor it and find the remainder. It ends up being 3x^5 -7x^3-11x^2 +2 = 3x^4 + 6x^3 +5x^2-x-2 before finding the remainder of -2.

Answer 1

You are asked if x-2 is a factor,not to actually find the answer.
so...
f(2) =3(2^5) - 7(2^3) - 11(2^2) + 2
= 96 - 56 - 44+2
= -2

so, no, it is not

you were correct

Answer 2

Thank you