# Thread: Remainder, equation of a polynomial

1. ## Remainder, equation of a polynomial

What is the remainder when x^29 - 7x^14 + 8 is divided by x-1
you divide this with long division correct? is there a shorter way to do it??

Write the equation of a polynomial with real coefficients that has 2 and 2-i as zeros. not sure what to do on this..
thanks

2. Originally Posted by Murphie
What is the remainder when x^29 - 7x^14 + 8 is divided by x-1
you divide this with long division correct? is there a shorter way to do it??

Mr F says: Yes. Read this: The Remainder Theorem

Write the equation of a polynomial with real coefficients that has 2 and 2-i as zeros. not sure what to do on this..
thanks
The factors are (x - 2), (x - [2-i]) and .... (x - [2+i])

(this last factor follows from the conjugate root theorem).

Now multiply these factors together to get a polynomial that satisfies the given requirements.

Note that $(x - [2-i]) (x - [2+i]) = ([x - 2] + i) ([x - 2] - i) = [x - 2]^2 + 1^2 = \, ....$