ACT Question

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ACT Question for July 1st

What polynomial must be added to x² - 2x + 6 so that the sum is 3x² + 7x ?

A) 4x² + 5x + 6

B) 3x² + 9x + 6

C) 3x² + 9x - 6

D) 2x² + 9x - 6

E) 2x² - 5x + 6

Correct

Incorrect

The correct answer is (D).

Getting to the Answer: If the sum of the unknown polynomial and x²-2x+6 is 3x²+7x, then that polynomial equals (3x²+7x)-(x²-2x+6). Subtract the like terms individually:

3x²-x²=2x²

7x-(-2x)=7x+2x=9x

0-6=-6

Thus, the unknown polynomial is 2x²+9x-6.