How to Factor

What is a Quadratic Expression A quadratic expression is an expression where the largest exponent for a variable is 2. Ex:

What is a Quadratic Expression A quadratic expression can come in different forms. FormGeneral FormExample Standard Form Factored Form

Standard Form a, b & c are numbers that are called “coefficients”

Factored Form r & s are numbers

What is Factoring Factoring is the process for turning a “standard” form expression into a “factored” form expression

What is Factoring A quadratic expression in standard form can also sometimes be called a “trinomial” when it has three terms term #1term #2term #3

4 Types of Trinomials 1.Simple Trinomial 2.Simple Trinomial with Common Factoring 3.Complex Trinomial 4.Complex Trinomial with Common Factoring

Simple Trinomial - (a=1) A trinomial who’s “a” value is 1

Simple Trinomial Simple Trinomial with Common Factoring A trinomial who’s “a” value is 1 after a common factor is removed. Now a simple trinomial By common factoring

Complex Trinomial - (a≠1) A trinomial who’s “a” value is NOT 1

Complex Trinomial Complex Trinomial with Common Factoring A trinomial who’s “a” value is NOT 1 after a common factor is removed. Now a complex trinomial By common factoring

Which is Which? What types of trinomial is below:

Factoring a Simple Trinomial 1.Write out the factors of the “c” in pairs. Factored! 2.Now chose a pair whose numbers can be added or subtracted to make the “b” value 3.Use these two numbers to make the factors of the expression

Factoring a Simple Trinomial 1.Write out the factors of the “c” in pairs. cbcb 2.Now chose a pair whose numbers can be added or subtracted to make the “b” value 3.Use these two numbers to make the factors of the expression

Factoring a Simple Trinomial 1.Write out the factors of the “c” in pairs. cbcb 2.Now chose a pair whose numbers can be added or subtracted to make the “b” value 3.Use these two numbers to make the factors of the expression

Factoring a Complex Trinomial 2.Write out the factors of the “ac” in pairs. ac b 3.Now chose a pair whose numbers can be added or subtracted to make the “b” value 1.Multiply the “a” and “c” values.

Factoring a Complex Trinomial 3.Now chose a pair whose numbers can be added or subtracted to make the “b” value 4.Split the “bx” into two terms using the factor pairs from above. 5.Common factor the first two terms and then factor the second two terms. 6.Place the two terms multiplying the brackets into a factor 7.The other factor is the terms inside the brackets