Answer:
A) -x² - 7x + 14
Step-by-step explanation:
Pre-Solving
We are given the following functions:
f(x) = 2x² - 3x + 6
g(x) = 3x² + 4x - 8
We want to find what f(x) - g(x) is.
f(x) - g(x) means that we subtract the value of g(x) from the value of f(x).
Solving
We can substitute 2x² - 3x + 6 for f(x) and 3x² + 4x - 8 for g(x).
We get:
2x² - 3x + 6 - (3x² + 4x - 8)
Notice the parentheses around 3x² + 4x - 8 (the value of g(x)). They are there because 3x² + 4x - 8 is the entire value of g(x), and we need to make sure that each term that makes up g(x) is subtracted from our value of f(x), which is the 2x² - 3x + 6.
- If we didn't include the parentheses, it would seem like the minus sign was only on the 3x², not the entire polynomial.
We can distribute the minus sign (which is really just -1) to each term.
We get:
2x² - 3x + 6 - 3x² - 4x + 8
Now, combine like terms.
-x² - 7x + 14
The answer is A.
