Question

The polynomial 10x3 + 35x2 − 4x − 14 is factored by grouping.

10x3 + 35x2 − 4x − 14


5x2(____) − 2(____)


What is the common factor that is missing from both sets of parentheses?


-a-...−2x − 7

-b-...2x + 7

-c-...−2x2 + 7

-d-...2x2 + 7

Answer 1

Answer is 2x+7 because in the first parenthesis when you take out 5x2 you are left with 2x+7 and in the 2nd parenthesis you also get 2x+7 because the negative is factored out

Answer 2

Answer: the coomon factor that is missing from both sets of parentheses is 2x + 7.

Step-by-step explanation:

These are the steps to factor the polynomial with the reasons that justify them:

Step Reason

1. 10x³ + 35x² - 4x - 14 Given

2. (10x³ + 35x²) - (4x + 14) Group the terms

3. 5x² (2x + 7) - 2 (2x + 7) Common factor 5x² and 2

After this, you extract common factor 2x + 7 and have the complete factored polynomial: (2x + 7) (5x² - 2).