Advanced Factoring Strategies for Quadratic Expressions

Examples, solutions, and videos to help Algebra I students learn how to develop strategies for factoring quadratic expressions that are not easily factorable, making use of the structure of the quadratic expression.

New York State Common Core Math Algebra I, Module 4, Lesson 3, Lesson 4

Worksheets for Algebra 1

Lesson 3 Summary
A polynomial expression of degree is often referred to as a quadratic expression.
Some quadratics are not easily factored. The following hints will make the job easier:

• In the difference of squares, a² − b², either of these terms a or b could be a binomial itself.
• The product-sum method is useful, but can be tricky when the leading coefficient is not 1.
• Trial and error is a viable strategy for finding factors.

Check your answers by multiplying the factors to ensure you get back the original quadratic expression.

Lesson 3 Exercises

Factor the expanded form of these quadratic expressions. Pay particular attention to the negative and positive signs.

Lesson 3 Problem Set Sample Solutions

Factor the following quadratic expressions.

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Lesson 4 Opening Exercises

Factor the following quadratic expressions:
6x² + 5x - 6
6x² + 7x - 20
-4x² - 4x - 1

Lesson 4 Summary

While there are several steps involved in splitting the linear term, it is a relatively more efficient and reliable method for factoring trinomials in comparison to simple guess-and-check.

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