Problem of the Week

Updated at Nov 25, 2024 5:58 PM

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Mar 24, 2025

This week we have another algebra problem:

How would you find the factors of $21{v}^{2}-2v-3$ ?

Let's start!

21{v}^{2}-2v-3

Split the second term in

21{v}^{2}-2v-3

into two terms.

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

21\times -3=-63

Ask: Which two numbers add up to

-2

and multiply to

-63

7

and

-9

Split

-2v

as the sum of

7v

and

-9v

21{v}^{2}+7v-9v-3

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21{v}^{2}+7v-9v-3

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

7v(3v+1)-3(3v+1)

Factor out the common term

3v+1

(3v+1)(7v-3)

Done