Problem of the Week

Updated at Jan 21, 2019 3:48 PM

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Mar 31, 2025

This week we have another algebra problem:

How can we factor $10{x}^{2}-19x-15$ ?

Let's start!

10{x}^{2}-19x-15

Split the second term in

10{x}^{2}-19x-15

into two terms.

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

10\times -15=-150

Ask: Which two numbers add up to

-19

and multiply to

-150

6

and

-25

Split

-19x

as the sum of

6x

and

-25x

10{x}^{2}+6x-25x-15

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10{x}^{2}+6x-25x-15

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

2x(5x+3)-5(5x+3)

Factor out the common term

5x+3

(5x+3)(2x-5)

Done