Question

Use the remainder therom to find the remainder when x^4-3x^2-9x+4 is divided by x-3

Answer 1

If we can write the given polynomial as


`\underbrace{p(x)}_{\text{given}}=q(x)(x-3)+r(x)`

that is, write
`p(x)` as the product of two factors plus some remainder term, then we can simply plug in
`x=3` to determine the remainder term because that would force the
`q(x)` term to vanish.


`p(x)=x^4-3x^2-9x+4\implies p(3)=31`

so the remainder upon dividing
`p(x)` by
`x-3` is 31.