PSAT Math Multiple-Choice Question 685: Answer and Explanation

Question: 685

(3x³ - 2x² + 5x + 7) - (x⁴ + x(x + 2)) = ?

• A. 2x³ - x² + 7x + 9
• B. -x⁴ + 3x³ - x² + 7x +7
• C. 2x⁴ - 3x² + 5x + 5
• D. -x⁴ + 3x³ - 3x² + 3x + 7

Correct Answer: D

Explanation:

(D) First, distribute the x in the second part of the expression:

x⁴ + x(x + 2) = x⁴ + x² + 2x

Next, distribute the negative sign:

(3x³ - 2x² + 5x + 7) - (x⁴ + x² + 2x) = 3x³ - 2x² + 5x + 7 - x⁴ -x² - 2x

Next, combine like terms:

3x³ - 2x² + 5x + 7 - x⁴ - x² - 2x = 3x³ - 3x² + 3x + 7 - x⁴

Rearrange the terms in descending order:

-x⁴ + 3x³ - 3x² + 3x + 7

So choice (D) is correct.