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# A2-A-2-1

last edited by 5 years, 1 month ago

A2.A.2.1 Factor polynomial expressions including but not limited to trinomials, differences of squares, sum and difference of cubes, and factoring by grouping using a variety of tools and strategies.

In a Nutshell

Students will use their existing knowledge of factoring to build on the process of factoring polynomials. They will identify an appropriate method for factoring a variety of polynomials  including, but not limited to, trinomials, differences of squares, and sums and differences of cubes. Strategies they might apply include distributive property, technology and the Factor Theorem, factoring by grouping, product and sum, slide and divide, patterns for special polynomials, such as differences of squares, differences or sums of cubes, and perfect square trinomials.

## Teacher Actions

• Students will develop strategies and use an appropriate procedure to find the factors of given polynomials.
• Students will develop accurate procedural fluency to factor a polynomial expression.

• Students will develop a conceptual understanding of a factorable versus non-factorable polynomial.

• Students will develop a productive mathematical disposition as they look for and make use of patterns to memorize the formulas for the differences of squares, perfect square trinomials, and the sums and differences of cubes.

• Implement tasks that allow students to  explore and solve problems that build on their knowledge of factoring.

• Implement tasks that provide multiple entry points and allow the students opportunities to find the factors of a variety of polynomials.

• Select tasks that help students build fluency factoring polynomials and recognizing when they are not factorable.

• Ensure students check factors by posing purposeful questions about their results.

## Misconceptions

• Recognize a polynomial expression may be factored by various methods.

• Factor a trinomial expression correctly and check answer against original expression.

• Recognize and factor a sums or differences of cubes.

• Recognize and factor a difference of squares.

• Identify when to factoring by grouping and implement it when appropriate.

• Students do not recognize differences of squares.

• Students fail to check middle term when finding factors.

• Students do not recognize sums or differences of cubes.

• When using sum or difference of cubes factoring patterns, students place signs in the wrong place.

• Students associate the sum/difference of cubes as the cube of a sum/difference. For example: a3-b3  = (a - b)

• Students put terms in the incorrect order to factor by grouping.

OKMath Framework Introduction