Solving Equations by Factoring Keeper 5 GSE Honors Algebra II

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.

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

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

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

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

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

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

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

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

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

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

Example: Solve by factoring. 40 𝑥 2 +312𝑥+217=−7

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

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