How do you divide #(x^2-5x-5x^3+x^4)div(5+x)# using synthetic division?

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Answer 1 · 2016-12-05T08:13:05

The remainder is #=1300# and the quotient is #=x^3-10x^2+51x-260#

Rearrange the polynomials in decreasing powers of #x#

Let's do the long division

#color(white)(aaaa)##x^4-5x^3+x^2-5x##color(white)(aaaa)##∣##x+5#

#color(white)(aaaa)##x^4+5x^3##color(white)(aaaaaaaaaaaaa)##∣##x^3-10x^2+51x-260#

#color(white)(aaaa)##0-10x^3+x^2#

#color(white)(aaaaaa)##-10x^3-50x^2#

#color(white)(aaaaaaaaaa)##0+51x^2-5x#

#color(white)(aaaaaaaaaaaa)##+51x^2+255x#

#color(white)(aaaaaaaaaaaaaaaa)##0-260x#

#color(white)(aaaaaaaaaaaaaaaaaa)##-260x-1300#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaa)##0+1300#

You can use the remainder theorem

#f(x)=x^4-5x^3+x^2-5x#

#f(-5)=625+625+25+25=1300#