Question

Let f(x) = 7x2 - 5x + 3 and g(x) = 2x2 + 4x - 6.

Part A: Find f(x) + g(x)

Part B: Find f(x) - g(x)

Part C: Find g(x) - f(x)

Answer 1

Part A)
`f(x)+g(x)=9x^(2)-x-3`

Part B)
`f(x)-g(x)=5x^(2)-9x+9`

Part C)
`g(x)-f(x)=-5x^(2)+9x-9`

Explanation:

we have

`f(x)=7x^(2) -5x+3`

`g(x)=2x^(2)+4x-6`

Part A) Find f(x) + g(x)

`f(x)+g(x)=(7x^(2) -5x+3)+(2x^(2)+4x-6)`

Group terms that contain the same variable

`f(x)+g(x)=(7x^(2)+2x^(2))+(-5x+4x)+(3-6)`

Combine like terms

`f(x)+g(x)=(9x^(2))+(-x)+(-3)`

`f(x)+g(x)=9x^(2)-x-3`

Part B) Find f(x)- g(x)

`f(x)-g(x)=(7x^(2) -5x+3)-(2x^(2)+4x-6)`

`f(x)-g(x)=(7x^(2) -5x+3)-2x^(2)-4x+6`

Group terms that contain the same variable

`f(x)-g(x)=(7x^(2)-2x^(2))+(-5x-4x)+(3+6)`

Combine like terms

`f(x)-g(x)=(5x^(2))+(-9x)+(9)`

`f(x)-g(x)=5x^(2)-9x+9`

Part C) Find g(x)- f(x)

`g(x)-f(x)=(2x^(2)+4x-6)-(7x^(2) -5x+3)`

`g(x)-f(x)=(2x^(2)+4x-6)-7x^(2)+5x-3`

Group terms that contain the same variable

`g(x)-f(x)=(2x^(2)-7x^(2))+(4x+5x)+(-6-3)`

Combine like terms

`g(x)-f(x)=(-5x^(2))+(9x)+(-9)`

`g(x)-f(x)=-5x^(2)+9x-9`