I need help in dividing polynomials. I get some problems but my teacher doesnt explain enough. Help Me?

Question

(p^3-6)/(p-1)
(t^3-6t^2+1)/(t+2)
(x^5-1)/(x-1)
(2x^3-5x^2+4x-4)/(x-2)

Answer 1

When you divide polynomials, you have to put in all the missing terms. For example, in the first problem, you need to think about it as being:
(p^3 + 0 p^2 + 0 p - 6)/(p-1)

Divide the p^3 by p and you get p^2, which is your first term. Multiply p^2*(p-1) = p^3-p^2. Subtract that from p^3 + 0 p^2 + 0 p - 6 and you get p^2 + 0 p - 6.

Now divide the p^2 by p and you get p, which is your second term. Multiply p*(p-1) and you get p^2-p. Subtract that from p^2 + 0 p - 6 and you get p-6.

Now divide p by p and you get 1, which is your third term. Multiply 1(p-1) = p-1. Subtract that from p-6 and you get -5. You can't divide -5 by p so that is your remainder.

Therefore your answer is

p^2+p+1 Remainder -5

or

p^2+p+1-5/(p-1)

That's the basic technique. Just remember to fill in any missing powers of the variable with a term that has zero as the coefficient (the leading number). You don't have to do that with the second and fourth problems, but you do with the third.

Hope that helps.

PS Synthetic division makes this easier, but you can't use the technique until they teach it to you!

Answer 2

you can use synthetic division. like for the first example:
since p-1, use 1 as the factor and line up the coefficients from (p^3-6):

1 0 0 -6
1 1 1
1 1 1 -5

the answer then is: p^2 + p + 1 remainder. -5.

Answer 3

OK what are the problems ?

write one out and show me the problem