Question

How do you divide `6x^342+18x^63-5x^2-20` by `x-1`?

Answer 1

You can't

Explanation:

If `x-1` is a factor then the value of `x=1` will give 0
`6+18-5-20=-1` so `x-1` can't be a factor

Answer 2

Using synthetic division, it's not so bad. But I don't know how to format division here.

Explanation:

It goes something like this:

`{:(342, 341, 340, " . . . ", 64, 63, 62, " . . . ", 3, 2, 1,"cst"), (6,0,0," . . . ",0,18,0," . . . ",0,-5,0,-20),( color(white)"SS", 6, 6, " . . . ", 6, 6, 24, " . . . ", 24, 24, 19, 19),(6, 6, 6, " . . . ", 6, 24, 24, " . . . ", 24, 19, 19, -1):}`

The quotient is:
`6x^341+6x^340 + 6x^339+* * * +6x^63+24x^62+24x^61 + * * * +24x^2+19x+19`:

The remainder is `-1`.
(Which is nice, because it is easy to see that the expression evaluates at `x=1` to `-1` so that agrees with the remainder, as the Remainder Theorem tells us they will.)

Answer 3

-1 is the remainder

Explanation:

For this i recommend Euclid lemma

`p(x) = q(x)(x-1) + r(x)`

`p(1) = r(x)`

Now we get that `r(x) = -1`

Now `p(x) = q(x)(x-1) -1`

`=>`we can divide `(p(x) + 1)/( x-1)`

Now `p'(x) = 6x^342+18x^63-5x^2-19`

I believe you question is to find the remainder if not I think you do what Jim is proposing