Problem of the Week

Updated at Oct 19, 2020 8:38 AM

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Mar 24, 2025

This week we have another algebra problem:

How can we compute the factors of $2{v}^{2}+9v-5$ ?

Let's start!

2{v}^{2}+9v-5

Split the second term in

2{v}^{2}+9v-5

into two terms.

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

2\times -5=-10

Ask: Which two numbers add up to

9

and multiply to

-10

10

and

-1

Split

9v

as the sum of

10v

and

-v

2{v}^{2}+10v-v-5

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2{v}^{2}+10v-v-5

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

2v(v+5)-(v+5)

Factor out the common term

v+5

(v+5)(2v-1)

Done