Problem of the Week

Updated at May 29, 2017 10:13 AM

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Mar 24, 2025

This week we have another algebra problem:

How would you find the factors of $5{x}^{2}-14x-3$ ?

Let's start!

5{x}^{2}-14x-3

Split the second term in

5{x}^{2}-14x-3

into two terms.

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

5\times -3=-15

Ask: Which two numbers add up to

-14

and multiply to

-15

1

and

-15

Split

-14x

as the sum of

x

and

-15x

5{x}^{2}+x-15x-3

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5{x}^{2}+x-15x-3

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

x(5x+1)-3(5x+1)

Factor out the common term

5x+1

(5x+1)(x-3)

Done