3.4 Solve by Factoring (Part 1)

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

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

GCF (Greatest Common Factor)

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

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.

Example:

Homework Factoring Worksheet