Overcoming a Second Obstacle in Factoring—What If There Is a Remainder?

Overcoming a Second Obstacle in Factoring—What If There Is a Remainder?

Student Outcomes

• Students rewrite simple rational expressions in different forms, including representing remainders when dividing.

New York State Common Core Math Algebra II, Module 1, Lesson 18

Worksheets for Algebra II, Module 1, Lesson 18

Opening Exercise

Write the rational number 13/4 as a mixed number.

Example 1

a. Find the quotient by factoring the numerator.
(𝑥2 + 3𝑥 + 2) / (2𝑥 + 2)
b. Find the quotient
(𝑥2 +3𝑥 + 5) / (𝑥 + 2)

Example 2

a. Find the quotient by factoring the numerator.
b. Find the quotient.

Exercises 1–10

Find each quotient by inspection.
Find each quotient by using the reverse tabular method.
Find each quotient by using long division.
Rewrite the numerator in the form (𝑥 −ℎ)2 + 𝑘 by completing the square. Then find the quotient.

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