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.
Terms introduced in this lesson:
Teaching Strategies and Tips
a=1,b>0,c>0. See Examples 1-4.
a=1,b<0,c>0. See Examples 5 and 6.
a=1,c<0. See Examples 7-9.
- Allow students to infer that if c>0(a=1), then the factorization will be either of the form (−−+−−)(−−+−−) or (−−−−−)(−−−−−) (same signs). If c<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.