AnswersCommon Core Algebra I B-ICFactoring Polynomials: Double Grouping — Unit testQuestion 4
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Factoring Polynomials: Double Grouping — Unit test

Question 4 • Common Core Algebra I B-IC

Mrs. Ishimitsu is installing a rubber bumper around the edge of her coffee table. The dimensions of the rectangular table are (2x2 – 16) feet and (–x2 + 4x + 1) feet. Which expression represents the total perimeter of the table, and if x = 3, what is the length of the entire rubber bumper?

Answer
A
x2 + 4x – 15; 3 feet
B
x2 + 4x – 15; 6 feet
C
2x2 + 8x – 30; 6 feet
D
2x2 + 8x – 30; 12 feet

Explanation

Add the side lengths and multiply by 2: 2[(2x² − 16) + (−x² + 4x + 1)] = 2x² + 8x − 30. When x = 3, the perimeter is 2(3²) + 8(3) − 30 = 18 + 24 − 30 = 12 feet, so the correct choice is 2x² + 8x − 30; 12 feet.

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