How do you divide (x^4 - 3x - 5)/(x+2)?

1 Answer
Tony B
Aug 8, 2016

x^3-2x^2+4x-11+17/(x+2)

Explanation:

Note that I use place keepers that have no value. This is done to make sure things line up properly. Example-> 0x^2

Numerator" "->" "x^4+0x^3+0x^2-3x-5
color(magenta)(x^3)(x+2)" "->" "ul(x^4+2x^3)" "larr" Subtract"
" "0-2x^3+0x^2-3x-5
color(magenta)(-2x^2)(x+2)" "->" "ul( -2x^3-4x^2)" "larr" Subtract"
" "0+4x^2-3x-5
" "color(magenta)(4x)(x+2) " "->" "ul(4x^2+8x)" "larr" Subtract"
" "0-11x-5
color(magenta)(-11)(x+2)" "->" "ul(-11x-22 )" "larr" Sub."
" "0+17

Where the final value of color(magenta)("17 is the remainder")

(x^4-3x-5)/(x+2) = color(magenta)(x^3-2x^2+4x-11+17/(x+2))

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