Problem of the Week

Updated at Sep 4, 2017 9:39 AM

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Mar 24, 2025

To get more practice in algebra, we brought you this problem of the week:

How can we factor $6{x}^{2}+3x-30$ ?

Check out the solution below!

6{x}^{2}+3x-30

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

6{x}^{2}

3x

, and

-30

It is

3

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

6{x}^{2}

3x

, and

-30

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

3

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

GCF =

3

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

3(\frac{6{x}^{2}}{3}+\frac{3x}{3}-\frac{30}{3})

Simplify each term in parentheses.

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

Split the second term in

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

into two terms.

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

2\times -10=-20

Ask: Which two numbers add up to

1

and multiply to

-20

5

and

-4

Split

x

as the sum of

5x

and

-4x

2{x}^{2}+5x-4x-10

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

3(2{x}^{2}+5x-4x-10)

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

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

Factor out the common term

2x+5

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

Done