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

3 Answers
Jun 17, 2015

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

Jun 19, 2015

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.)

Nov 15, 2015

-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