Final answer:
Amir subtracted the quantity 2x² + 8x - 12 from the polynomial 3x² + 8x - 16 to result in the expression x² - 4.
Step-by-step explanation:
The student is asking what quantity was subtracted from the polynomial 3x² + 8x - 16 to get the resulting expression x² - 4.
To find this, we set up an equation where the original polynomial minus some unknown quantity (which we'll call Q) equals the resulting expression:
3x² + 8x - 16 - Q = x² - 4
To solve for Q, we rearrange the equation:
Q = (3x² + 8x - 16) - (x² - 4)
Now, we combine like terms:
Q = (3x² - x²) + (8x) + (-16 + 4)
Q = 2x² + 8x - 12
Therefore, the quantity Amir subtracted was 2x² + 8x - 12.