Special Factoring Strategies

Posted: August 26th, 2021

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Special Factoring Strategies

The two special factoring strategies selected here are the difference of squares and the perfect square trinomial. The main feature of binomial expressions is that they have two terms, while trinomials contain three terms(Karr 189). Factoring these expressions requires special strategies. Both the difference of squares and perfect square trinomial strategies are discussed the following with examples for illustrating how the strategies are implemented.

Difference of Squares

For faster factoring of expression of either form, it is always necessary to check whether it is binomial or a trinomial. Besides, it is essential to check a polynomial expression, whether it is a difference of squares(Straighterline). A difference of squares refers to a binomial expression of the following form:

Notably, the first and last terms are perfect squares. When factoring a difference of squares, the following are the results:

, the reason is that. For example.

Perfect Square Trinomials

Just as in the difference of the square method, it is always necessary to recognize patterns existing in trinomial expression. This involves checking whether a trinomial is a perfect square, usually taking the following form:. Notably, the first and the last terms in such an expression are the perfect squares, and the middle term coefficient is two times square root of the last term multiplied by the square root of the first term coefficient(Karr 216; Straighterline). A factored perfect squared trinomial gives the following results:

However, perfect square trinomial can also take the following form:As such, it is factored as follows: . For example, given a trinomial expression: . The solution will be: . Hence, perfect square trinomials are the results from squaring binomials.

Works Cited

Karr, Rosemary M., Marilyn B. Massey, and R D. Gustafson. Beginning and intermediate algebra: a guided approach. Stamford, CT: Cengage Learning, 2015. Print.

Straighterline. Algebra: Factoring trinomials when the leading coefficient is 1. YouTube, May 19, 2020: https://www.youtube.com/watch?v=11GsZJB1f34