# What is the standard form of  y= (3x-5)(x+1)(x-2) ?

Dec 4, 2017

$\textcolor{b l u e}{y = 3 {x}^{3} - 8 {x}^{2} - x + 10}$

#### Explanation:

We have the factors given to us

$y = \left(3 x - 5\right) \left(x + 1\right) \left(x - 2\right)$

We will focus on the factors on the right hand side of the equation.

We can use the FOIL Method to multiply the binomials .

Multiply the $\textcolor{red}{F}$irst terms.
Multiply the $\textcolor{red}{O}$uter terms.
Multiply the $\textcolor{red}{I}$nner terms.
Multiply the $\textcolor{red}{L}$ast terms.

We will keep the first factor as it is, but multiply the last two factors to get:

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

$\Rightarrow \left(3 x - 5\right) \left({x}^{2} - x - 2\right)$

Net we will multiply these two factors to get:

$3 {x}^{3} - 3 {x}^{2} - 6 x - 5 {x}^{2} + 5 x + 10$

$\Rightarrow 3 {x}^{3} - 8 {x}^{2} - x + 10$

So, we have

$\textcolor{b l u e}{y = 3 {x}^{3} - 8 {x}^{2} - x + 10}$

which is the required polynomial in standard form.

I hope that helps.