1. Solving Equations by Factoring
Keeper 5
GSE Honors Algebra II

2. Solving Polynomial Equations:
Steps:
1.) Equation must = 0 & write in standard form.
*Standard Form = Exponents in Descending Order
2.) Factor using the appropriate method.
*Remember to start by taking out a GCF if possible.
3.) Set each factor = 0 and solve.
The Zero Product Property says that if a polynomial equals zero, then the factors of the polynomial equal zero.
*The highest exponent in the problem, called the degree, should equal the number of solutions you get.

3. Example: Solve by factoring.
4 𝑥 2 −2𝑥=0

4. Example: Solve by factoring.
6 𝑥 2 +𝑥=2

5. Example: Solve by factoring.
𝑥 3 +9 𝑥 2 =−20𝑥

6. Example: Solve by factoring.
39 𝑛 2 −156𝑛=−3 𝑛 2 −90

7. Example: Solve by factoring.
9 𝑥 2 −118𝑥+42=−7 𝑥 2

8. Example: Solve by factoring.
7 𝑥 2 −17𝑥+14=4 𝑥 2 −6

9. Example: Solve by factoring.
10 𝑥 2 −7𝑥+1=0

10. Example: Solve by factoring.
8𝑥−5=−4 𝑥 2

11. Example: Solve by factoring.
6 𝑥 2 +7𝑥=20

12. Example: Solve by factoring.
27 𝑥 2 −3𝑥+2=5𝑥+2− 𝑥 2

13. Example: Solve by factoring.
40 𝑥 𝑥+217=−7

14. Example: Solve by factoring.
15 𝑥 2 −34𝑥+15=0

15. Example: Solve by factoring.
10 𝑥 2 −9𝑥=9