FACTORING SIMPLE EXPRESSIONS
DEFINITION: to factor an expression
To factor an expression means to take the expression and rename it as a product.

That is, to factor an expression means to write the expression as a product.

EXAMPLES:
Question: Factor: [beautiful math coming... please be patient]$\, ab + ac$
Solution: [beautiful math coming... please be patient]$ab + ac = a(b + c)$
The expression [beautiful math coming... please be patient]$\,ab + ac\,$ is a sum, since the last operation is addition.
The expression [beautiful math coming... please be patient]$\,a(b + c)\,$ is a product, since the last operation is multiplication.
The process of factoring took us from the sum [beautiful math coming... please be patient]$\,ab + ac\,$ to the product [beautiful math coming... please be patient]$\,a(b + c)\,$.

Notice that [beautiful math coming... please be patient]$\,\,ab + ac = a(b + c)\,\,$ is just the distributive law, backwards!

In going from the name [beautiful math coming... please be patient]$\,ab + ac\,$ to the name [beautiful math coming... please be patient]$\, a(b + c) \,$,
the common factor ([beautiful math coming... please be patient]$\,a\,$) is first identified, and written down.
Next, an opening parenthesis ‘ ( ’ is inserted.
Then, the remaining parts of each term are written down.
Finally, the closing parenthesis ‘ ) ’ is inserted.

Question: Write in factored form: [beautiful math coming... please be patient]$\,3x - 3t\,$
Solution: [beautiful math coming... please be patient]$3(x - t)$
Question: Write in factored form: [beautiful math coming... please be patient]$\,2xy - 2yz$
Solution: [beautiful math coming... please be patient]$ 2y(x - z)$
Question: Write in factored form: [beautiful math coming... please be patient]$\,5x^2 - x^2y^2$
Solution: [beautiful math coming... please be patient]$ x^2(5 - y^2) $
Note: In the exercises below, exponents are typed in using the ‘^’ key.
For example, [beautiful math coming... please be patient]$\, x^2(5 - y^2) \,$ is typed in as   x^2(5 - y^2) .
Question: Write in factored form: [beautiful math coming... please be patient]$\,x(2x + 1) - 3(2x + 1)$
Solution: [beautiful math coming... please be patient]$ (2x + 1)(x - 3) $
Note: The product [beautiful math coming... please be patient]$\,(2x+1)(x-3)\,$ can also be written as [beautiful math coming... please be patient]$\,(x-3)(2x+1)\,$.
There is no convention here about which name is ‘best’.
The exercise below recognizes both answers.
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Listing All the Factors of a Whole Number

 
 
Write in factored form:
    
(an even number, please)