Problem of the Week

Updated at Jan 29, 2018 1:35 PM

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Mar 31, 2025

This week's problem comes from the algebra category.

How can we compute the factors of $2{x}^{2}-15x+7$ ?

Let's begin!

2{x}^{2}-15x+7

Split the second term in

2{x}^{2}-15x+7

into two terms.

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

2\times 7=14

Ask: Which two numbers add up to

-15

and multiply to

14

-1

and

-14

Split

-15x

as the sum of

-x

and

-14x

2{x}^{2}-x-14x+7

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2{x}^{2}-x-14x+7

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

x(2x-1)-7(2x-1)

Factor out the common term

2x-1

(2x-1)(x-7)

Done