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

##### 1 Answer

Mar 7, 2016

#### 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)= 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

#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.