Problem of the Week

Updated at Jul 15, 2019 11:45 AM

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Mar 24, 2025

This week's problem comes from the algebra category.

How can we factor $15{x}^{2}-14x+3$ ?

Let's begin!

15{x}^{2}-14x+3

Split the second term in

15{x}^{2}-14x+3

into two terms.

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

15\times 3=45

Ask: Which two numbers add up to

-14

and multiply to

45

-5

and

-9

Split

-14x

as the sum of

-5x

and

-9x

15{x}^{2}-5x-9x+3

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15{x}^{2}-5x-9x+3

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

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

Factor out the common term

3x-1

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

Done