Problem of the Week

Updated at May 23, 2022 11:41 AM

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Mar 24, 2025

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

How can we compute the factors of $30{n}^{2}-59n+28$ ?

Here are the steps:

30{n}^{2}-59n+28

Split the second term in

30{n}^{2}-59n+28

into two terms.

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

30\times 28=840

Ask: Which two numbers add up to

-59

and multiply to

840

-24

and

-35

Split

-59n

as the sum of

-24n

and

-35n

30{n}^{2}-24n-35n+28

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30{n}^{2}-24n-35n+28

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

6n(5n-4)-7(5n-4)

Factor out the common term

5n-4

(5n-4)(6n-7)

Done