How do you simplify and divide #(t^5-3t^2-20)(t-2)^-1#?

1 Answer
Oct 15, 2017

Quotient #t^4+2t^3+8t^2+5t+10#, Remainder #=0#

Explanation:

#(t^5-3t^2-20)/(t-2)#
We will follow synthetic division method.

#2color(white)( aaa) |color(white)(a) 1 color(white)(aaa) 0 color(white)(aaa)0 color(white)(aaa)-3 color(white)(aaa) 0 color(white)(aaa) -20#
#color(white)(aaaa) | color(white)(aaaaa) 2 color(white)(aaa) 4 color(white)(aaaaa) 8 color(white)(aaa) 10 color(white)(aaaaa) 20#
#color(white)(aaaa) | …………………………………#
#color(white)( aaaaaaa) 1 color(white)(aaa) 2 color(white)(aaa) 8 color(white)(aaaaa) 5 color(white)(aaa) 10 color(white)(aaaaaa)0#

Quotient is #t^4+2t^3+8t^2+5t+10#, Remainder #=0