# Overcoming Obstacles in Factoring

### Overcoming Obstacles in Factoring

Student Outcomes

• Students will factor certain forms of polynomial expressions by using the structure of the polynomials.

### New York State Common Core Math Algebra II, Module 1, Lesson 12

Worksheets for Algebra II, Module 1, Lesson 12

Classwork

Example 1

Find all real solutions to the equation (𝑥2 − 6𝑥 + 3)(2𝑥2 −4𝑥 − 7) = 0.

Exercise 1

Factor and find all real solutions to the equation (𝑥2 − 2𝑥 − 4)(3𝑥2 + 8𝑥 − 3) = 0.

Exercise 2

Find all real solutions to 𝑥3 − 5𝑥2 − 4𝑥 + 20 = 0.

Exercise 3

Find all real solutions to 𝑥3 − 8𝑥2 − 2𝑥 + 16 = 0.

Lesson Summary In this lesson, we learned some techniques to use when faced with factoring polynomials and solving polynomial equations.

• If a fourth-degree polynomial can be factored into two quadratic expressions, then each quadratic expression might be factorable either using the quadratic formula or by completing the square.
• Some third-degree polynomials can be factored using the technique of factoring by grouping.

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