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

Mar 7, 2016

$f \left(x\right) = {x}^{3} - 4 {x}^{2} + 8 x - 1$

#### 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

$f \left(x\right) = x {\left(x - 2\right)}^{2} + 4 x - 5$

$f \left(x\right) = x \textcolor{b l u e}{\left(x - 2\right) \left(x - 2\right)} + 4 x - 5$

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

$f \left(x\right) = x \textcolor{b l u e}{\left({x}^{2} - 2 x - 2 x + 4\right)} + 4 x - 5$
$f \left(x\right) = x \left(\textcolor{b l u e}{{x}^{2} - 4 x + 4}\right) + 4 x - 5$

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

$f \left(x\right) = {x}^{3} - 4 {x}^{2} + 4 x + 4 x - 5$

4) Now combine all like terms to get

$f \left(x\right) = {x}^{3} - 4 {x}^{2} + 8 x - 1$

Now, our function is in the standard form.