Lesson 9.8 Factor Polynomials Completely Essential Question: How do you factor polynomials completely?

Before we start… 𝑦 1 =4 𝑥 2 −12 𝑦 2 =4 𝑥 2 −3 𝑦 1 =4 𝑥 2 −12 𝑦 2 =4 𝑥 2 −3 𝑦 3 =𝑥 𝑥−3 +5 𝑥−3 𝑦 4 = 𝑥−3 𝑥+5

Factor 2𝑥 𝑥+4 −3 𝑥+4

Factor 3 𝑦 2 𝑦−2 +5 𝑦−2

Factor 𝑥 𝑥−2 + 𝑥−2

Factor 4𝑦 𝑦−3 +5 𝑦−3

Factor by Grouping Polynomials with four terms can sometimes be factored by grouping terms. Group the terms into pairs and look for common factors.

How do you factor by grouping? Group the terms. Factor each group. Find the common factor of the two new terms.

Factor Completely When we factor an expression, the result can sometimes be factored further. A polynomial that is factored completely is written as a product of unfactorable polynomials.

How do you factor completely? Factor out a GCF. Factor the remaining polynomial. Trinomials Difference of squares Perfect square trinomials By grouping

Factor completely 𝑛 2 +2𝑛−1

Factor completely 4𝑥 3 −44 𝑥 2 +96𝑥

Factor completely 50 ℎ 4 −2 ℎ 2

Factor completely 3𝑥 3 −12𝑥

Factor completely 𝑚 3 −2 𝑚 2 −8𝑚

Factor completely 2𝑥 2 −4𝑥−30

Factor completely −𝑥 2 +10𝑥−21

Factor completely 𝑏 3 −5 𝑏 2 −4𝑏+20

Solve 𝑤 3 −8 𝑤 2 +16𝑤=0

Solve 𝑥 3 −25𝑥=0

Solve 𝑐 3 −7 𝑐 2 +12𝑐=0

How do you factor polynomials completely?

Ticket Out the Door Factor 𝑥 3 + 𝑥 2 +2𝑥+2