9.5: Factoring Quadratic Expressions
Learning Objectives
At the end of this lesson, students will be able to:
 Write quadratic equations in standard form.
 Factor quadratic expressions for different coefficient values.
 Factor when
a=−1 .
Vocabulary
Terms introduced in this lesson:
 quadratic polynomial
 quadratic trinomials
Teaching Strategies and Tips
In this lesson, students learn to factor quadratic polynomials according to the signs of

a=1,b>0,c>0 . See Examples 14.
Additional Examples:
Factor.
a.
b.
c.

a=1,b<0,c>0 . See Examples 5 and 6.
Additional Examples:
Factor.
a.
b.
c.

a=1,c<0 . See Examples 79.
Additional Examples:
Factor.
a.
b.
c.

a=−1 . See Example 10.
Additional Examples:
Factor.
a.
b.
c.
 Allow students to infer that if
c>0(a=1) , then the factorization will be either of the form(−−+−−) (−−+−−) or(−−−−−) (−−−−−) (same signs). Ifc<0 (a=1) , then use the form(−−−−−) (−−−−−) (different signs).  See summary at the end of the lesson for a list of procedures and examples for each case.
Emphasize that factoring is the reverse of multiplication.
 Use an example such as
(x+3)(x+7)=x2+10x+21 in which the binomials are expanded one step at a time to motivate factoring.  Demonstrate that factoring is equivalent to putting squares and rectangles back together into larger rectangles.
Example:
Multiply.
Solution. The diagram shows that
Suggest that students stop listing the possible products for
Error Troubleshooting
General Tip: For quadratic trinomials with