Explain the process of factoring expressions and see how factoring is used to solve certain types of equations.

Answer 1

To factor an expression, you may want to find the GCF (greatest common factor) to take out of the expression of multiple terms have that expression. This can make simplifying the expression more manageable with smaller numbers/variables that are easier to work with.

For example:

Let's factor this expression:

10x - 60

Can we find the GCF (greatest common factor) of 10 and 60?

10: 1, 2, 5, 10

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

They both have the factor 10 in common!

Lets take 10 out of our expressions:

10(x - 6)

Another reason to factor an expression is when you are solving quadratic equations. Factoring from standard form to factored form allows us to work with the length and width of our algebra square to find the two x-intercepts.

For example:

x²+7x+12 = 0

To factor, we need to find two numbers that will add to 8 (the "b" value), and also multiply to 12 (the "c" value).

First, let's list out the factors of 12:

1, 2, 3, 4, 6, 12

3 and 4 would multiply to 12 and also add to 7!

So to factor,

(x+3)(x+4) = 0

Now, we can solve with just one step equations:

x+3=0 x+4=0

-3 -3 -4 -4

x = -3 x = -4

I hope this was helpful in answering your question!