Problem of the Week

Updated at Oct 2, 2017 9:33 AM

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Mar 31, 2025

This week we have another algebra problem:

How can we factor $35{x}^{2}-50x+15$ ?

Let's start!

35{x}^{2}-50x+15

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

35{x}^{2}

-50x

, and

15

It is

5

What is the highest degree of $x$ that divides evenly into

35{x}^{2}

-50x

, and

15

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

5

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GCF =

5

Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

5(\frac{35{x}^{2}}{5}+\frac{-50x}{5}+\frac{15}{5})

Simplify each term in parentheses.

5(7{x}^{2}-10x+3)

Split the second term in

7{x}^{2}-10x+3

into two terms.

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

7\times 3=21

Ask: Which two numbers add up to

-10

and multiply to

21

-3

and

-7

Split

-10x

as the sum of

-3x

and

-7x

7{x}^{2}-3x-7x+3

To get access to all 'How?' and 'Why?' steps, join Cymath Plus!

5(7{x}^{2}-3x-7x+3)

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

5(x(7x-3)-(7x-3))

Factor out the common term

7x-3

5(7x-3)(x-1)

Done