Lesson 6-5: Solving Polynomial Equations
Past Target
Present Target
Future Target
I can solve quadratic functions by
I will factor polynomials.
I will use strategies including
factoring.
factoring to transform and solve
I will solve polynomial equations
polynomial equations.
by factoring.
Sum of two cubes: 𝑎3 + 𝑏 3
Difference of two cubes: 𝑎3 − 𝑏 3
If a polynomial cannot be factored it is called a ____________________ polynomial.
Ex 1: Factor each sum or difference of cubes.
a. 𝑥 3 − 8
b. 𝑎3 + 27
c. 𝑥 6 −125
Factoring Polynomials
for any # of terms,
look for
GCF
for 2 terms, check for:
for 3 terms, check for:
for 4 or more terms, check for:
Difference of two squares
Perfect square trinomial
Grouping
Sum of two cubes
Sum and Product Factors
Difference of two cubes
Ex 2: CUBES - Factor. If the polynomial cannot be factored, write prime.
a. 24𝑥 5 + 3𝑥 2 𝑦 3
b. 𝑥 3 − 400
Ex 3: GROUPING - Factor. If the polynomial cannot be factored, write prime.
a. 𝑥 3 + 5𝑥 2 − 2𝑥 − 10
b. 8𝑎𝑥 + 4𝑏𝑥 + 4𝑐𝑥 + 6𝑎𝑦 + 3𝑏𝑦 + 3𝑐𝑦
Ex 4: SQUARES - Factor. If the polynomial cannot be factored, write prime.
a. 16𝑥 4 − 1
b. 64𝑥 6 − 𝑦 6
Ex 5: QUADRATIC FORM (2-1-NONE) – Rewrite each expression in quadratic form. Factor.
a. 𝑥 4 − 7𝑥 2 + 12
b. 2𝑥 6 + 7𝑥 3 + 3
Ex 6: Solve by factoring.
a. 𝑥 4 − 29𝑥 2 + 100 = 0
b. 𝑥 3 = 5𝑥 2