What is the standard form of a polynomial (2x^2-6x-5)(3-x)?

Apr 15, 2016

The standard for is $\text{ } y = - 2 {x}^{3} + 12 {x}^{2} - 13 x - 15$

Explanation:

Using the distributive property of multiplication:

Given: color(brown)((2x^2-6x-5)color(blue)((3x-x))

$\textcolor{b r o w n}{2 {x}^{2} \textcolor{b l u e}{\left(3 - x\right)} - 6 x \textcolor{b l u e}{\left(3 - x\right)} - 5 \textcolor{b l u e}{\left(3 - x\right)}}$

Multiply the contents of each bracket by the term to the left and outside.

I have grouped the products in the square brackets so you can see more easily the consequence of each multiplication.

$\left[6 {x}^{2} - 2 {x}^{3}\right] + \left[- 18 x + 6 {x}^{2}\right] + \left[- 15 + 5 x\right]$

Removing the brackets

$6 {x}^{2} - 2 {x}^{3} - 18 x + 6 {x}^{2} - 15 + 5 x$

Collecting like terms

$\textcolor{red}{6 {x}^{2}} \textcolor{b l u e}{- 2 {x}^{3}} \textcolor{g r e e n}{- 18 x} \textcolor{red}{+ 6 {x}^{2}} - 15 \textcolor{g r e e n}{+ 5 x}$

$\implies \textcolor{b l u e}{- 2 {x}^{3}} \textcolor{red}{+ 12 {x}^{2}} \textcolor{g r e e n}{- 13 x} - 15$

So the standard for is $\text{ } y = - 2 {x}^{3} + 12 {x}^{2} - 13 x - 15$