PSAT Math Multiple-Choice Question 482: Answer and Explanation

Question: 482

–(x² – 2) + x⁴ + (2x² – 8)

Which of the following expressions is equivalent to the expression above?

• A. x⁴ + x² – 6
• B. x⁴ + x² – 10
• C. x⁴ – x² – 10
• D. 2x⁸ – 6

Correct Answer: A

Explanation:

A

The question asks for an equivalent form of the provided expression. Use Bite-Sized Pieces and Process of Elimination to tackle this question. Begin with the integer term in the first set of parentheses, –2, and combine it with the like term in the second set of parentheses, paying attention to sign changes: –(–2) + (–8) = 2 – 8 = –6. Choices (B) and (C) can be eliminated since they do not contain this term. One difference between (A) and (D) is the x⁴ term. In the original expression, there is only one term with a power of 4, and it is not multiplied or raised to a power, so this term will remain as is. Eliminate (D), which doesn't contain an x⁴ term. The correct answer is (A).