Factor the following polynomial by Grouping Show your work E

Factor the following polynomial by Grouping: (Show your work) Explain how you know when to factor out a negative sign from the last two terms.

12x^3+15x^2-8x-10

Explain how you know when to factor out a negative sign from the last two terms.

Solution

Group:
(12x^3 + 15x^2) -(8x + 10)

Factor out the common factors:
3x^2 (4x + 5) - 2 (4x + 5)

Use the distributive property:
(4x +5) (3x^2 - 2)

The quadratic remaining in parentheses doesn\'t factor any farther in real or rational numbers, so presumably you\'re finished.

When in the first group you find (4x+5) as a factor, you know that in order to make it common among the two groups, you need to take the negative sign out.