Respuesta :
We have three functions
[tex]\begin{gathered} f(x)=2x^2+5x-3 \\ g(x)=-x^2-4x+2 \\ h(x)=-x^2+4x-2 \end{gathered}[/tex]We need to find which expression give us
[tex]3x^2=x-1[/tex]Let us start with the first expression
f(x) + h(x)
[tex]2x^2+5x-3+(-x^2+4x-2)[/tex]Let us add the like terms
[tex](2x^2_{}+-x^2)+(5x+4x)+(-3+\text{ -2)}[/tex][tex]x^2+9x+-5=x^2+9x-5[/tex]Let us find the second expression
[tex]f(x)-h(x)=2x^2+5x-3-(-x^2+4x-2)[/tex]The 2nd bracket must be multiplied by (-)
[tex]2x^2+5x-3+x^2-4x+2[/tex]Add the like term
[tex](2x^2+x^2)+(5x-4x)+(-3+2)[/tex][tex]3x^2+x+-1=3x^2+x-1[/tex]The answer is B
If you try the other answer they will be wrong
In g(x) + f(x) the first terms are -x^2+2x^2 = x^2
So it is not our answer because the first term is 3x^2
In g(x) - h(x) the first terms are -x^2 - (-x^2) = -x^2+ x^2 = 0
So also it is not our answer
In h(x) - f(x) the first terms are -x^2 - 2x^2 = -3x^2
So it is not our answer
In f(x) + g( x) the first terms are 2x^2 + (-x^2) = x^2
So it is not our answer
The correct answer is B
