One factor of x^3+2x^2-11x-12 is x+4. Find the remaining factors.

a. x+1, x+3
b. x-1, x+3
c. x+1, x-3
d. x-1, x-3

I think you need to divide the polynomial by x+4

I think you need to divide the polynomial by x+4.

also, look at the sign of the 12 term. Since you have x+4 given, then one of the two remaining factors has to have a negative which means d and a cannot be correct.

got it! thanks

To find the remaining factors, we can use polynomial long division or synthetic division.

Let's use synthetic division to divide the given polynomial (x^3 + 2x^2 - 11x - 12) by the factor (x + 4):

-4 | 1 2 -11 -12
|__-4__8___12
1 -2 -3 0

The resulting quotient is x^2 - 2x - 3.

To find the remaining factors, we need to factor the quadratic equation, x^2 - 2x - 3.

We can use factoring or the quadratic formula to find the factors of x^2 - 2x - 3:

Using factoring:

x^2 - 2x - 3 = (x + 1)(x - 3)

So the remaining factors are (x + 1) and (x - 3).

Therefore, the correct answer is option c) x + 1, x - 3.