Problem of the Week

Updated at Jun 21, 2021 4:30 PM

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Mar 31, 2025

This week's problem comes from the algebra category.

How can we factor $30{t}^{2}+17t-21$ ?

Let's begin!

30{t}^{2}+17t-21

Split the second term in

30{t}^{2}+17t-21

into two terms.

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

30\times -21=-630

Ask: Which two numbers add up to

17

and multiply to

-630

35

and

-18

Split

17t

as the sum of

35t

and

-18t

30{t}^{2}+35t-18t-21

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30{t}^{2}+35t-18t-21

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

5t(6t+7)-3(6t+7)

Factor out the common term

6t+7

(6t+7)(5t-3)

Done