Problem of the Week

Updated at May 6, 2024 10:11 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 $5{u}^{2}-39u+28$ ?

Here are the steps:

5{u}^{2}-39u+28

Split the second term in

5{u}^{2}-39u+28

into two terms.

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

5\times 28=140

Ask: Which two numbers add up to

-39

and multiply to

140

-4

and

-35

Split

-39u

as the sum of

-4u

and

-35u

5{u}^{2}-4u-35u+28

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5{u}^{2}-4u-35u+28

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

u(5u-4)-7(5u-4)

Factor out the common term

5u-4

(5u-4)(u-7)

Done