How do we long divide #10x^4-14x^3-10x^2+6x-10# by #x^3-3x^2+x-2# and what are the quotient and remainder?

1 Answer
Dec 22, 2017

#10x^4-14x^3-10x^2+6x-10#

= #(x^3-3x^2+x-2)(10x+16)+28x^2+10x+22#

Explanation:

#" Quotient"darr#
#x^3-3x^2+x-2)bar(10x^4-14x^3-10x^2+6x-10)(10x+16#
#" "ul(10x^4-30x^3+10x^2-20x)darr#
#" "16x^3-20x^2+26x-10#
#" "ul(16x^3-48x^2+16x-32)#
#"Remainder "-> " "28x^2+10x+22#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hence, quotient is #10x+16#, remainder is #28x^2+10x+22# and

#10x^4-14x^3-10x^2+6x-10#

= #(x^3-3x^2+x-2)(10x+16)+28x^2+10x+22#