Question

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

Answer 1

The standard for is `" "y=-2x^3+12x^2-13x-15`

Explanation:

Using the distributive property of multiplication:

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

`color(brown)(2x^2color(blue)((3-x))-6xcolor(blue)((3-x))-5color(blue)((3-x)) )`

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.

`[6x^2-2x^3]+[ -18x+6x^2]+[-15+5x]`

Removing the brackets

`6x^2-2x^3 -18x+6x^2-15+5x`

Collecting like terms

`color(red)(6x^2)color(blue)(-2x^3)color(green)( -18x)color(red)(+6x^2)-15color(green)(+5x)`

`=>color(blue)(-2x^3)color(red)(+12x^2)color(green)(-13x)-15`

So the standard for is `" "y=-2x^3+12x^2-13x-15`