Problem of the Week

Updated at Oct 23, 2023 1:29 PM

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Mar 31, 2025

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

How can we compute the factors of $28{z}^{2}+45z-7$ ?

Check out the solution below!

28{z}^{2}+45z-7

Split the second term in

28{z}^{2}+45z-7

into two terms.

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

28\times -7=-196

Ask: Which two numbers add up to

45

and multiply to

-196

49

and

-4

Split

45z

as the sum of

49z

and

-4z

28{z}^{2}+49z-4z-7

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28{z}^{2}+49z-4z-7

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

7z(4z+7)-(4z+7)

Factor out the common term

4z+7

(4z+7)(7z-1)

Done