To find [tex]\( g(x) - h(x) \)[/tex] given the functions [tex]\( g(x) \)[/tex] and [tex]\( h(x) \)[/tex], follow these steps:
1. Write down the given functions:
[tex]\( g(x) = x^2 + 4x \)[/tex]
[tex]\( h(x) = 3x - 5 \)[/tex]
2. Set up the expression for [tex]\( g(x) - h(x) \)[/tex]:
[tex]\( g(x) - h(x) = (x^2 + 4x) - (3x - 5) \)[/tex]
3. Distribute the negative sign across the terms in [tex]\( h(x) \)[/tex]:
[tex]\( - (3x - 5) = -3x + 5 \)[/tex]
4. Combine the expressions:
[tex]\( g(x) - h(x) = x^2 + 4x - 3x + 5 \)[/tex]
5. Simplify by combining like terms:
Combine the [tex]\( x \)[/tex]-terms: [tex]\( 4x - 3x = x \)[/tex]
So, [tex]\( g(x) - h(x) = x^2 + x + 5 \)[/tex]
Therefore, the correct expression for [tex]\( g(x) - h(x) \)[/tex] is:
[tex]\[ g(x) - h(x) = x^2 + x + 5 \][/tex]
The correct answer is:
[tex]\[ g(x) - h(x) = x^2 + x + 5 \][/tex]
