Question

What is the standard form of `f(x)=x(x-2)^2+4x-5`?

Answer 1

`f(x)= x^3 -4x^2 +8x-1`

Explanation:

The standard form of an polynomial function is written in descending order.

1) For this problem, we need to expand the function like this

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

`f(x)= xcolor(blue)((x-2)(x-2))+4x-5`

2) Let's foil aka multiply and combine like terms

`f(x)= xcolor(blue)((x^2 -2x-2x+4)) +4x-5`
`f(x)= x(color(blue)(x^2-4x+4))+4x-5`

3) Let's distribute `x` into the function to get

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

4) Now combine all like terms to get

`f(x)= x^3 -4x^2 +8x-1`

Now, our function is in the standard form.