Sorting Polynomials by Factoring Methods

6.6.4 Sorting Polynomials by Factoring Methods

6.6.4 • Sorting Polynomials by Factoring Methods

Cool Down

Examine the following polynomials:
$27 q^{2} - 3$
$x^{2} - 10 x + 25 - y^{2}$
$16 x^{2} - 72 x + 81$
$36 y^{2} + 12 y + 1$
$4 p^{2} - 100$
$x^{2} + 12 x + 36 - y^{2}$

Sort the polynomials by whether you would factor them using the difference of squares or the perfect square trinomial method.

Draw a table similar to this on a sheet of paper. Record your results. If a polynomial requires both methods, place it in both columns.

Difference of Squares Method	Perfect Square Trinomial Method

Compare your answers:

Difference of Squares Method	Perfect Square Trinomial Method
$27 q^{2} - 3$ $4 p^{2} - 100$ $x^{2} - 10 x + 25 - y^{2}$ $x^{2} + 12 x + 36 - y^{2}$	$16 x^{2} - 72 x + 81$ $36 y^{2} + 12 y + 1$ $x^{2} - 10 x + 25 - y^{2}$ $x^{2} + 12 x + 36 - y^{2}$

Difference of Squares Method

Perfect Square Trinomial Method

$27 q^{2} - 3$

$4 p^{2} - 100$

$x^{2} - 10 x + 25 - y^{2}$

$x^{2} + 12 x + 36 - y^{2}$

$16 x^{2} - 72 x + 81$

$36 y^{2} + 12 y + 1$

$x^{2} - 10 x + 25 - y^{2}$

$x^{2} + 12 x + 36 - y^{2}$

Why Should I Care?

Illustration of a woman wearing an orange apron arranging a bouquet of flowers at a table, surrounded by vases, flower arrangements, scissors, and string, with a floral picture on the wall behind her.

Ozzie Gomez and Juan Casava own a store called Plant Shop Chicago. They use polynomials everyday to make sure the operations of their small business go smoothly.

One of the most important parts of running a business is understanding where your money is going. You need to know how much you are spending and how much you are making. For example, Ozzie Gomez and Juan Cassava can use polynomials to calculate how many different plants they can buy and how much money they can make off of each sale.