Question

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

Answer 1

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