" Dividend" div "divisor" = "quotient" Dividend÷divisor=quotient
(6x^2+x-7)div(2x+3) = (3x-4) " remainder 5"(6x2+x−7)÷(2x+3)=(3x−4) remainder 5
The dividend must be in descending powers of x.
In long division: repeat the pattern:
Divide color(magenta)(2x)2x into the term with highest index available
Multiply by both terms at the side
Subtract (change the signs)
Bring down the next term
color(white)(xxxx)ulcolor(white)(xxxxx)ul(color(red)(3x)color(blue)(-4))
color(magenta)(2x)+3 )6x^2+x-7 " "6x^2 divcolor(magenta)(2x) = color(red)(3x)
color(white)(xxxx)ulcolor(red)(-6x -9x)" "darr " multiply and subtract"
color(white)(xxxxxxx)-8x -7" "-8x divcolor(magenta)(2x)= color(blue)(-4)
color(white)(xxxxxxxxx)ulcolor(blue)(8x+12)" multiply and subtract"
color(white)(xxxxxxxxxxxxx)5" remainder"
