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.