Question

Which of the following is a factor of f(x) = 3x3 + 8x2 − 87x + 28?

Answer 1

I think that the answer you chose is not correct...

Answer 2

if you have a trouble actually factoring the polynomial, then I would (perhaps) suggest dividing the polynomial you got by each of the answer-choices....

Answer 3

And the answer-choice (when used as divisor), that would not yeild any (nonzero) remainder, that would be the answer-choice that is a factor of the polynomial.

Answer 4

If x - k is a factor, then k is a zero of the polynomial.

Answer 5

Evaluate the polynomial for each given value.
If it evaluates to zero, then it is a factor.

Answer 6

Keep in mind the form of the factors is x - k.
In the first choice, you have x - 1/4, so evaluate the polynomial for x = 1/4.
In choice B, you have x + 1/4. That means you need to evaluate the polynomial
for x = -1/4.
In choice C use x = 4.
In choice D use x = -4.

Answer 7

so I plug each into the equation?

Answer 8

Evaluate the polynomial for those values of x until the polynomial evaluates to zero. That that will be the value of the zero and the corresponding factor.

Answer 9

Yes. Plug in each value.

Answer 10

You can narrow it down before you do all that work.
Do you know the Rational Roots Theorem?

Answer 11

ive heard of it

Answer 12

If you use the Rational Roots Theorem, you can eliminate 2 of the 4 choices, so you will only have to test 2 of the choices instead of all 4.

Answer 13

If you have a polynomial with integer coefficients, then the roots must have the form of a factor of the constant term over a factor of the leading coefficient.