SSAT Math Question 400: Answer and Explanation

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Question: 400

11. Combine and simplify:

(6x⁵ – 2x³ + 8) – (4x⁵ – x⁴ + 3x² + 12)

A. 2x⁵ – x⁴ – x³ + 20
B. 2x⁵ – x⁴ + x³ – 4
C. 2x⁵ + x⁴ – 2x³ + 3x² – 4
D. 2x⁵ + x⁴ – 5x³ + 20

Correct Answer: E

Explanation:

The only like terms involve the fifth-degree exponent and the numbers without variables: 6x⁵ – 4x⁵ = 2x⁵, and 8 – 12 = 4. For the remaining elements, be careful about signs: distribute the negative sign to obtain x⁴, –2x³ remains as is, and distribute the negative sign to obtain –3x². Put the elements in descending order of power: 2x⁵ + x⁴ – 2x³ – 3x² – 4.

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