Problem of the Week

Updated at Jul 17, 2017 8:05 AM

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Mar 24, 2025

This week's problem comes from the algebra category.

How can we compute the factors of $42{x}^{2}+43x-7$ ?

Let's begin!

42{x}^{2}+43x-7

Split the second term in

42{x}^{2}+43x-7

into two terms.

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

42\times -7=-294

Ask: Which two numbers add up to

43

and multiply to

-294

49

and

-6

Split

43x

as the sum of

49x

and

-6x

42{x}^{2}+49x-6x-7

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42{x}^{2}+49x-6x-7

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

7x(6x+7)-(6x+7)

Factor out the common term

6x+7

(6x+7)(7x-1)

Done