Question

What is the standard form of `y=(3-x)(x-1)^2`?

Answer 1

`-x^3+5x^2-7x+3`

Explanation:

`"expand the factors and collect like terms"`

`(x-1)^2=(x-1)(x-1)larrcolor(blue)"expand using FOIL"`

`(x-1)(x-1)=x^2-2x+1`

`"now multiply expansion by factor "(3-x)`

`(3-x)(x^2-2x+1)`

`"multiply each term in the second factor by each term"`
`"in the first factor"`

`color(red)(3)(x^2-2x+1)color(red)(-x)(x^2-2x+1)`

`=3x^2-6x+3-x^3+2x^2-xlarrcolor(blue)"collect like terms"`

`=-x^3+5x^2-7x+3larrcolor(red)"in standard form"`

`"to express a polynomial in "color(blue)"standard form"`

`"start with the term with the largest exponent of the variable"`
`"followed by terms of decreasing exponents in descending"`
`"order"`