Question which-

2.4 Equivalent Expressions - Simplifying polynomials
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Which of the following is equivalent to 2 x cubed, plus 4 ?

A.

4 times open parenthesis, x cubed, plus 4, close parenthesis

B.

4 times open parenthesis, x cubed, plus 2, close parenthesis

C.

2 times open parenthesis, x cubed, plus 4, close parenthesis

D.

2 times open parenthesis, x cubed, plus 2, close parenthesis

Which of the following is equivalent to ?

Easy-difficulty · SAT Math · Equivalent Expressions — Simplifying polynomials. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice D is correct. The expression 2 x cubed, plus 4 has two terms, 2 x cubed and 4. The greatest common factor of these two terms is 2. Factoring 2 from each of these terms yields 2 times x cubed, plus, 2 times 2, or 2 times, open parenthesis, x cubed plus 2, close parenthesis.

Choices A and B are incorrect because 4 is not a factor of the term 2 x cubed. Choice C is incorrect and may result from factoring 2 from 2 x cubed but not from 4.