Given the binomials (x + 1), (x + 4), (x - 5), and (x - 2), which one is a factor of f(x) = 3x3 - 12x2 - 4x - 55?

(x + 1)

(x + 4)

(x - 5)

(x - 2)

Step-by-step explanation:

The Factor Theorem tells us that substituting  into a polynomial    when divided by a linear factor   will give us a value of 0 IF   is a factor of the polynomial

So, checking each of the 4 binomials, and getting a 0 as answer will tell us which one is a factor of the function given.

Putting  for into the function:

NOT a factor.

Putting  for into the function:

NOT a factor.

Putting  for into the function:

IS a factor.

Putting  for into the function:

NOT a factor.

So we can see that only    is a factor.

For this case we have the following polynomial:

The first thing we must do is factor the polynomial.

We have then:

Therefore, we observe that the common factor factor of the polynomial is:

The common factor factor of the given function is:

replication and blocking

step-by-step explanation: