Problem of the Week

Updated at Oct 16, 2017 9:29 AM

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Mar 10, 2025

To get more practice in algebra, we brought you this problem of the week:

How can we compute the factors of $7{x}^{2}-44x+12$ ?

Check out the solution below!

7{x}^{2}-44x+12

Split the second term in

7{x}^{2}-44x+12

into two terms.

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

7\times 12=84

Ask: Which two numbers add up to

-44

and multiply to

84

-2

and

-42

Split

-44x

as the sum of

-2x

and

-42x

7{x}^{2}-2x-42x+12

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7{x}^{2}-2x-42x+12

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

x(7x-2)-6(7x-2)

Factor out the common term

7x-2

(7x-2)(x-6)

Done