Problem of the Week

Updated at Oct 29, 2018 9:27 AM

Recent Posts

Mar 31, 2025

How can we factor $6{x}^{2}+33x-18$ ?

Below is the solution.

6{x}^{2}+33x-18

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

6{x}^{2}

33x

, and

-18

It is

3

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

6{x}^{2}

33x

, and

-18

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{33x}{3}-\frac{18}{3})

Simplify each term in parentheses.

3(2{x}^{2}+11x-6)

Split the second term in

2{x}^{2}+11x-6

into two terms.

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

2\times -6=-12

Ask: Which two numbers add up to

11

and multiply to

-12

12

and

-1

Split

11x

as the sum of

12x

and

-x

2{x}^{2}+12x-x-6

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

3(2{x}^{2}+12x-x-6)

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

3(2x(x+6)-(x+6))

Factor out the common term

x+6

3(x+6)(2x-1)

Done