Question

Let f(x)=2x^2 + 5x - 3, g(x)= -x^2 - 4x + 2, and h(x)= -x^2 + 4x - 2. Select all expresions that are equivalent to 3x^2 = x - 1.A. f(x) + h(x) B. f(x) - h(x)C. g(x) + f(x)D. g(x) - h(x)E. h(x) - f(x)F. f(x) + g(x)

Answer 1

We have three functions

`\begin{gathered} f(x)=2x^2+5x-3 \\ g(x)=-x^2-4x+2 \\ h(x)=-x^2+4x-2 \end{gathered}`

We need to find which expression give us

`3x^2=x-1`

Let us start with the first expression

f(x) + h(x)

`2x^2+5x-3+(-x^2+4x-2)`

Let us add the like terms

`(2x^2_{}+-x^2)+(5x+4x)+(-3+\text{ -2)}`
`x^2+9x+-5=x^2+9x-5`

Let us find the second expression

`f(x)-h(x)=2x^2+5x-3-(-x^2+4x-2)`

The 2nd bracket must be multiplied by (-)

`2x^2+5x-3+x^2-4x+2`

Add the like term

`(2x^2+x^2)+(5x-4x)+(-3+2)`
`3x^2+x+-1=3x^2+x-1`

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