Question

HELP PLEASE

Which expressions represents f(x)-g(x)?
f(x) = 2x^2 - 3x + 6
g(x) = 3x^2 + 4x - 8

A) -x^2 - 7x + 14
B) -5x^2 - x +2

Answer 1

The answer is A do you need an explanation? Sorry if I’m late

Answer 2

A) -x² - 7x + 14

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.