How do you divide [4x^2-3x+1]/(3+x)4x2−3x+13+x?

1 Answer
EZ as pi
Aug 9, 2016

[4x^2-3x+1]/(x+3) = (4x-15) " remainder " 464x2−3x+1x+3=(4x−15) remainder 46

Explanation:

color(red)[4x^2-3x+1]/color(blue)(x+3)4x2−3x+1x+3

In each line, divide xx into the term with the highest power of xx
Write the answer at the top.

4x^2 div x = 4x4x2÷x=4x
" " 4x-15 4x−15
" "x+3bar(|" "color(red)(4x^2 -3x" "+1)) x+3¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯∣∣ 4x2−3x +1
color(brown)(4x(x-2)->)" "underline(4x^2+12x)" " larr" Subtract
" "0 " "-15x
color(brown)(15(x-2))->" "underline(15x-45) larr Subtract
color(brown)("Remainder") ->" "0+46

:. [4x^2-3x+1]/(x+3) = (4x-15) " remainder " 46

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