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Factoring out the GCF and trinomials where the 3rd term is negative

Author: Elizabeth Dollhopf

How to use the distributive property backwards

On a separate sheet of paper, copy the following problems and factor out the GCF for each of the polynomials

1. $12 x to the power of 4 plus 6 x cubed minus 30 x squared$

2. $75 x to the power of 8 minus 50 x cubed$

3. $15 x cubed minus 40 x squared plus 35$

Focusing on the sign of the constant term to decide how to factor trinomials.

On the same sheet of paper as the last three problems, factor these:

4. $x squared minus 5 x minus 14$

5. $x squared plus 9 x minus 22$

6. $x squared minus 6 x minus 40$

Combining various factoring techniques in order to find the complete factorization.

Include these on your homework sheet. Factor the following

7. $3 x squared minus 15 x minus 18$

8. $4 x cubed y minus 49 x y cubed$

Bonus! State how many factors each of the above polynomials has.