Problem of the Week

Updated at Jul 3, 2023 9:26 AM

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Mar 31, 2025

For this week we've brought you this algebra problem.

How can we compute the factors of $25{z}^{2}-40z+12$ ?

Here are the steps:

25{z}^{2}-40z+12

Split the second term in

25{z}^{2}-40z+12

into two terms.

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

25\times 12=300

Ask: Which two numbers add up to

-40

and multiply to

300

-10

and

-30

Split

-40z

as the sum of

-10z

and

-30z

25{z}^{2}-10z-30z+12

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25{z}^{2}-10z-30z+12

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

5z(5z-2)-6(5z-2)

Factor out the common term

5z-2

(5z-2)(5z-6)

Done