How do you divide #(x^2-5x-12)div(x-3)#?
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#(x^2-5x-12)div(x-3) = (x-2) " rem "-18#
This can also be written as
#(x^2-5x-12)div(x-3) = (x-2) - 18/(x-3)#
The algebraic long division follows the same method as arithmetic long division...
#("dividend")/("divisor") = "quotient"#
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Write the dividend in the 'box' making sure that the indices are in descending powers of x.
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Divide the first term in divisor into the term in the dividend with the highest index. Write the answer at the top,
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Multiply it by BOTH terms of the divisor at the side
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Subtract - remember to change signs
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Bring down the next term
Repeat steps 2 to 5
#color(white)(xxxxxxxxxx)color(red)(x)color(blue)(-2) " "rem -18#
#color(white)(x)x-3 |bar( x^2 -5x -12)" "larr x^2divx = color(red)(x)#
#color(white)(xxxxxx)ul(color(red)(x^2-3x))" "darr" "larr# subtract (change signs)
#color(white)(xxxxxxxx) -2x-12""larr# bring down the -12,#-2x div x = color(blue)(-2)#
#color(white)(xxxxxxxx.)ul(color(blue)(-2x+6))" "larr# subtract (change signs)
#color(white)(xxxxxxxxxxx)-18 " "larr#remainder
#(x^2-5x-12)div(x-3) = (x-2) " rem "-18#
This can also be written as
#(x^2-5x-12)div(x-3) = (x-2) - 18/(x-3)#
