Question

Write a polynomial function rule for g(x)+f(x)

Consider the polynomial function
f(x)=7x^3+x2-4x+10
g(x)=c^2-5

Answer 1

Given:

Consider the given polynomials are:

`f(x)=7x^3+x^2-4x+10`

`g(x)=x^2-5`

To find:

The polynomial function rule for
`g(x)+f(x)`.

Solution:

We need to add both functions to get
`g(x)+f(x)`.

`g(x)+f(x)=(x^2-5)+(7x^3+x^2-4x+10)`

`g(x)+f(x)=x^2-5+7x^3+x^2-4x+10`

On combining like terms, we get

`g(x)+f(x)=7x^3+(x^2+x^2)-4x+(10-5)`

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

Therefore, the required function is
`g(x)+f(x)=7x^3+2x^2-4x+5`.