Question

Given P(x) = 2x3 - 11x2 + 18x - 15 is divided by x – 3. Use synthetic division to find the quotient and the remainder.

Answer 1

You can find the remainder right away by simply plugging in
`x=3`. The polynomial remainder theorem guarantees that the value of
`p(3)` is the remainder upon dividing
`p(x)` by
`x-3`, but I digress...

Synthetic division yields

3 | 2 -11 18 -15
. | 6 -15 9
- - - - - - - - - - - - - - - - -
. | 2 -5 3 -6

which translates to


`(2x^3-11x^2+18x-15)/(x-3)=2x^2-5x+3-\frac6{x-3}`

(and note that
`p(3)=2(3)^3-11(3)^2+18(3)-15=-6`, as expected)