Question

I’m not sure how to solve 3d. College calculus 1

Answer 1

See below

Explanation:

f(x) = ( x^2 + 5)^3 f(0) = 5^3 = 125

(x^2+5)^3 = x^6 + 15x^4 + 75 x^2 + 125

so you have (x^6 + 15x^4 + 75x^2 + 125 - 125) /x

= x^5 + 15x^3 + 75x = x ( x^4 + 15x^2 + 75)

Answer 2

Step 1

Given;

`f(x)=(x^2+5)^3`

Required; To simplify

`(f(x)-f(0))/(x),\text{ x}\\e0`

Step 2

`((x^2+5)^3-(0^2+5)^3)/(x)`

`(x^2+5)^3=(x^2)^3+3(x^2)^2(5)+3x^2(5^2)+5^3`
`(x^2+5)^3=x^6+15x^4+75x^2+125`
`((x^6+15x^4+75x^2+125)-125)/(x)`
`\begin{gathered} (x^6+15x^4+75x^2+125-125)/(x) \\ (x^6+15x^4+75x^2)/(x) \\ (f(x)-f(0))/(x)=x^5+15x^3+75x \end{gathered}`

Hence if we factorize we get;

`x(x^4+15x^2+75)`

Therefore;

`(f(x)-f(0))/(x)=x(x^4+15x^2+75)`