Answer:
Part A) [tex]f(x)+g(x)=9x^{2}-x-3[/tex]
Part B) [tex]f(x)-g(x)=5x^{2}-9x+9[/tex]
Part C) [tex]g(x)-f(x)=-5x^{2}+9x-9[/tex]
Step-by-step explanation:
we have
[tex]f(x)=7x^{2} -5x+3[/tex]
[tex]g(x)=2x^{2}+4x-6[/tex]
Part A) Find f(x) + g(x)
[tex]f(x)+g(x)=(7x^{2} -5x+3)+(2x^{2}+4x-6)[/tex]
Group terms that contain the same variable
[tex]f(x)+g(x)=(7x^{2}+2x^{2})+(-5x+4x)+(3-6)[/tex]
Combine like terms
[tex]f(x)+g(x)=(9x^{2})+(-x)+(-3)[/tex]
[tex]f(x)+g(x)=9x^{2}-x-3[/tex]
Part B) Find f(x)- g(x)
[tex]f(x)-g(x)=(7x^{2} -5x+3)-(2x^{2}+4x-6)[/tex]
[tex]f(x)-g(x)=(7x^{2} -5x+3)-2x^{2}-4x+6[/tex]
Group terms that contain the same variable
[tex]f(x)-g(x)=(7x^{2}-2x^{2})+(-5x-4x)+(3+6)[/tex]
Combine like terms
[tex]f(x)-g(x)=(5x^{2})+(-9x)+(9)[/tex]
[tex]f(x)-g(x)=5x^{2}-9x+9[/tex]
Part C) Find g(x)- f(x)
[tex]g(x)-f(x)=(2x^{2}+4x-6)-(7x^{2} -5x+3)[/tex]
[tex]g(x)-f(x)=(2x^{2}+4x-6)-7x^{2}+5x-3[/tex]
Group terms that contain the same variable
[tex]g(x)-f(x)=(2x^{2}-7x^{2})+(4x+5x)+(-6-3)[/tex]
Combine like terms
[tex]g(x)-f(x)=(-5x^{2})+(9x)+(-9)[/tex]
[tex]g(x)-f(x)=-5x^{2}+9x-9[/tex]
