# What is the standard form of f(x)=(2x-3)(x-2)^2+4x-5 ?

Sep 23, 2017

The standard form is $f \left(x\right) = 2 {x}^{3} - 11 {x}^{2} + 24 x - 17$

#### Explanation:

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

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

$f \left(x\right) = 2 {x}^{3} - 8 {x}^{2} + 8 x - 3 {x}^{2} + 12 x - 12 + 4 x - 5$ or

$f \left(x\right) = 2 {x}^{3} - 11 {x}^{2} + 24 x - 17$

A standard form of cubic equation is $f \left(x\right) = a {x}^{3} + b {x}^{2} + c x + d$ .

Here, the standard form is $f \left(x\right) = 2 {x}^{3} - 11 {x}^{2} + 24 x - 17$ Where

$a = 2 , b = - 11 , c = 24 \mathmr{and} d = = 17$ [Ans]