Problem of the Week

Updated at Mar 5, 2018 10:33 AM

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Mar 24, 2025

This week we have another algebra problem:

How can we factor $35{x}^{2}+29x-28$ ?

Let's start!

35{x}^{2}+29x-28

Split the second term in

35{x}^{2}+29x-28

into two terms.

Multiply the coefficient of the first term by the constant term.

35\times -28=-980

Ask: Which two numbers add up to

29

and multiply to

-980

49

and

-20

Split

29x

as the sum of

49x

and

-20x

35{x}^{2}+49x-20x-28

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35{x}^{2}+49x-20x-28

Factor out common terms in the first two terms, then in the last two terms.

7x(5x+7)-4(5x+7)

Factor out the common term

5x+7

(5x+7)(7x-4)

Done