1. 3.4 Solve by Factoring (Part 1)

2. Vocabulary
A monomial is an expression that is a number, a variable, or the product of a number and one or more variables.
Ex: 4, x, 4x, xy, 8xyz
A binomial is the sum or difference of two monomials.
Ex: 4 + x, xy + 8z, x – y  x + (-y)
A trinomial is the sum or difference of three monomials.
Ex: x + y + z, 4 – 2xy + 13z
A quadratic equation in one variable can be written as where a ≠ 0.
A solution of a quadratic equation is called the root or a zero of the equation or function.
Find solutions when the quadratic has an equal sign

3. Factoring: Remember to Completely Factor
When Factoring expressions, there is an order to follow when solving:
GCF
Greatest Common Factor
This is for any polynomial
Difference of Perfect Squares
Each term must be a perfect square
Coefficients must be perfect squares and even exponents on the variables
This is for only BINOMIALS
Reverse Foil
Finding the factors of the “C” term that when added together make the “B” term with the correct sign
Remember to Completely Factor

4. GCF (Greatest Common Factor)

5. Difference of Perfect Squares
Must be a Binomial
Must have subtraction between the terms

6. Reverse Foil Factoring
To factor an expression of the form
where a =1
Look for integers “r and s”
such that (r) (s) = c, and r + s = b.
Then use “r & s” in the factors of the expression.

7. Example:

8. Homework
Factoring Worksheet