ACT Question

Back Home

ACT Question for September 22nd

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.

(A) Incorrect: this adds x²-2x+6 to 3x²+7x instead of subtracting it from 3x²+7x

(B) Incorrect: this does not subtract the x² term and adds 6 instead of subtracting it

(C) Incorrect: this does not subtract the x² term

(D) Correct: this matches the correct calculation

(E) Incorrect: this has the correct value of 2x²; however, it incorrectly uses -7x-(-2x)=-5x and subtracts 6 rather than adding it