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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?


−2x − 7

2x + 7

−2x2 + 7

2x2 + 7

Verified Answer :

Neuron

If you would like to find the factor that is missing from both sets of parentheses, you can calculate this using the following step:

10x^3 + 35x^2 - 4x - 14 = 5x^2 (2x + 7) - 2 (2x + 7)

The correct result would be 2x + 7.

Eduard22sly

The common factor that is missing from both sets of parentheses is 2x + 7

How to determine the missing factor

To determine the missing factor, we would divide 10x³ + 35x² − 4x − 14 by 5x² – 2 using long division method as illustrated below

           2x + 7        

5x² – 2|10x³ + 35x² − 4x − 14

           –(10x³ – 4x)

            35x² – 14

          –(35x² – 14)

                   0

The result obtained from the division is 2x + 7.

Therefore, the missing factor is 2x + 7

Check

(5x² – 2)(2x + 7) = 5x²(2x + 7) – 2(2x + 7)

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