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

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Answer 1 · 2016-04-15T15:16:40

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

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 $" "y=-2x^3+12x^2-13x-15$

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