Question

Amir subtracted a quantity from the polynomiall 3x²+8x-16 and produced the expression x²-4 What quantity did Amir subtract? Explain how you got your answer. (Hint: 3x^2+8x-16 minus ? is going to = x^2-4)

A. -2x² + 8x + 12
B. 2x² - 8x +12
C. 2x²+8x-12
D. -2x² - 8x - 12

Answer 1

Amir subtracted the quantity 2x²+8x-12 from the polynomial 3x²+8x-16 to obtain the expression x²-4, making the correct answer option C.

Step-by-step explanation:

The student asked what quantity Amir subtracted from the polynomial 3x²+8x-16 to get x²-4. To find the subtracted quantity, we can set up an equation: the original polynomial minus the unknown quantity equals the resulting expression. So, let's call the unknown quantity 'Q':

3x²+8x-16 - Q = x²-4.

To find Q, rearrange the equation:

Q = (3x²+8x-16) - (x²-4).

Now simplify:

Q = 3x²+8x-16 - x²+4

Q = 2x²+8x-12

Therefore, the quantity Amir subtracted is 2x²+8x-12, which corresponds to option C.