Question

Given the polynomial functions f(x) and g(x) , find h(x) = f(x) - g(x) . f(x) = 4x ^ 4 - x ^ 3 + 3x ^ 2 + 6; g(x) = 5x ^ 3 - 2x ^ 2 + 3x - 2

Answer 1

Given:

`\begin{gathered} f(x)=4x^4-x^3+3x^2+6 \\ g(x)=5x^3-2x^2+3x-2 \\ h(x)=f(x)-g(x) \end{gathered}`
`\begin{gathered} h(x)=f(x)-g(x) \\ h(x)=4x^4-x^3+3x^2+6-(5x^3-2x^2+3x-2) \\ \text{Expanding the bracket with the negative sign,} \\ h(x)=4x^4-x^3+3x^2+6-5x^3+2x^2-3x+2 \\ \text{Collecting the like terms and then simplifying further;} \\ h(x)=4x^4-x^3-5x^3+3x^2+2x^2-3x+6+2 \\ h(x)=4x^4-6x^3+5x^2-3x+8 \end{gathered}`

Therefore,

`h(x)=4x^4-6x^3+5x^2-3x+8`

The SECOND OPTION is the correct answer.