PARCC algebra 2: write quotient as binomial

The following write-the-expression question, explained here in hopes of helping algebra 2 students in Maryland prepare for the PARCC test near the end of this school year, appears on the released version of the PARCC Algebra 2 sample items released following the 2016 test (#2).


Plots of 2x3+1 (blue) and 2x5+1 (orange)

Given the expression

\frac{4n^{2t}-1}{2n^t-1}

where t is an integer greater than or equal to 1,
write the expression as a binomial.

Solution strategy (there are others)

Analysis and resources for further study

Sal Khan, an engineer who launched the Khan Academy, discusses the FOIL rule as something mechanical you might just memorize. But, “when you’re 35, you’re not going to remember what FOIL means, and then you’re not going to be able to multiply this binomial,” he explains.

He then, more for commitment to long-term memory of how to multiply binomials, to explain the distributive property for multiplying binomials, which is also more logical, not a rote plug-and-play mnemonic.

The problem was perhaps a little easier than it needed to be to test this particular learning standard. As an additional challenge (if you’re game), write the binomial equivalent to the following expression:

\frac{16n^{2t}-64}{2n^t-4}
Correct answer

About the Author

Paul Katula

Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

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