Overcoming Obstacles in Factoring

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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 2

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.

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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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