\[2{x}^{2}y-8xy+6y\]

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Examples

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

2{x}^{2}y

-8xy

, and

6y

It is

2

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

2{x}^{2}y

-8xy

, and

6y

It is 1, since

x

is not in every term.

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

2{x}^{2}y

-8xy

, and

6y

It is

y

Multiplying the results above,

The GCF is

2y

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GCF =

2y

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

2y(\frac{2{x}^{2}y}{2y}+\frac{-8xy}{2y}+\frac{6y}{2y})

Simplify each term in parentheses.

2y({x}^{2}-4x+3)

Factor

{x}^{2}-4x+3

Ask: Which two numbers add up to

-4

and multiply to

3

-3

and

-1

Rewrite the expression using the above.

(x-3)(x-1)

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2y(x-3)(x-1)

Done

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