Question

using remainder theorem & synthetic division find p(r): P(x)=2x^4-3x^3+6, r=2

Answer 1

usually to find P(r) you need to plug in P(r)

Answer 2

make sure you use 0s as space holders

Answer 3

^4 3 2 1 0
------------ like this
2 -3 0 0 6

Answer 4

the remainder theorem says, if you divide P(x) by x-r
the remainder becomes P(r)

Answer 5

so all you do is synthetic division to find the remainder

Answer 6

2| 2 -3 0 0 6
0 4 2 4 8
---------------
2 1 2 4 14 <- remainder is 14
^^^^^^^^^^^

2r^3 +r^2 +2r +4 + 14(r-2)