What is the standard form of y=(3-x)(x-1)^2?
1 Answer
Nov 29, 2017
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"
