How do you use polynomial synthetic division to divide #(18x^2-15x-25)div(x-5/3)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?

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Answer 1 · 2017-12-30T10:43:13

The answer is #=(x-5/3)(18x+15)+0#

#color(white)(aaaa)##5/3##color(white)(aaaa)##|##18##color(white)(aaaa)##-15##color(white)(aaaa)##-25#

#color(white)(aaaa)##color(white)(aaaaaa)##|##color(white)(aaaaaaaa)##30##color(white)(aaaaaa)##25#

#color(white)(aaaa)##color(white)(aaaaaa)##|##18##color(white)(aaaaaa)##15##color(white)(aaaaaaa)##0#

Therefore,

#18x^2-15x-25=(x-5/3)(18x+15)+0#

The quotient is #=18x+15# and the remainder is #=0#