6
QuizMultiple Choice

Adding and Subtracting Polynomials

Question 6 • Common Core Algebra I B-IC

Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5?

Answer
A
The difference is a binomial with a degree of 5.
B
The difference is a binomial with a degree of 6.
C
The difference is a trinomial with a degree of 5.
D
The difference is a trinomial with a degree of 6.

Explanation

Subtract the second polynomial from the first: the a³b terms cancel, 9a²b² − (−3a²b²) = 12a²b², and −4ab⁵ − ab⁵ = −5ab⁵. The simplified difference has two terms, so it is a binomial. The term ab⁵ has degree 1 + 5 = 6, the greatest degree in the difference, so the correct choice is a binomial with a degree of 6.

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