Given one factor of the polynomial, factor the polynomial completely.

16. f (x) = x^3-4x^2-7x+10; x-5

17. g (x) = 2x^3+3x^2-23x-12; 2x+1

Use synthetic division to solve these problems

5 | 1 - 4 - 7 10

| v 5 5 - 10

1 1 - 2 0

This leads to x^2+x-2

Next we find what adds to 1 and multiplies to - 2

The factors of f (x) are 2 and - 1, written out as (x+2) and (x-1)

-1/2 | 2 3 - 23 - 12

| v - 1 - 1 12

2 2 - 24 0

This leads to 2x^2+2x-24

Next, multiply the 2 from the a value (since a is the value with x^2 and c is the value without any x) with - 24, which is - 48

Now find what adds to 2 and multiplies to - 48

The values for this are 8 and - 6, but keep in mind, when multiplying the value of a by c, you now have to add the values in place of what you tried adding it to, this time in the problem we found using synthetic division, in this case the 2 in the b value (the middle of the equation, or the value with only one x)

2x^2+8x-6x-24

When group factoring, you'd get 2x (x+4) - 6 (x+4)

So, the factors of g (x) are (x+4) and (2x-6)