Factoring Special Case Polynomials – Practice Problems

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Writing and factoring polynomials can have special cases. Learning to recognize these special cases is definitely worth your time because it may save you some hair pulling later on.

First is the square of binomials sums: (a + b)² = (a + b)(a + b) = a² + 2ab + b².

Similar to this case is the square of binomial differences: (a – b)² = (a – b)(a – b) = a² – 2ab + b².

The third special case is the difference of two squares: (a + b)(a – b) = a² – b².

Pay attention to the patterns of these three special cases and rather than spending time factoring, foiling, and distributing the terms, you will be doing a victory dance to celebrate how well you are doing in your Algebra class.

For example, if your teacher assigns you to factor this problem: x⁴ – 49. Whoa, this looks very difficult. Relax – it’s just the difference of two squares or a DOTS problem. (x²)² is equal to x⁴, and 7² is equal to 49, so to factor the difference of the two squares: (x² – 7) (x² + 7), and when you foil or use the distributive property, you are right back where you started: x⁴ – 49.

To see more examples of special case polynomials and have a laugh too, watch this video.

Understand the relationship between zeros and factors of polynomials.


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Exercises in this Practice Problem
Determine the area of the pool.
Calculate the area of each pool using the given values for $a$ and $b$.
Calculate the different possible sizes of the rose bed.
Find the carpet sizes using the FOIL method.
Explain the FOIL method for multiplication.
Use the product of binomials to calculate $43\times 37$.