- #1

auru

- 10

- 0

## Homework Statement

Find the monic greatest common divisor of two polynomials a = 6x

^{6}+ 12x

^{5}- 6x

^{4}-12x +12 and b = 3x

^{4}- 3.

## Homework Equations

The Euclidean Algorithm.

## The Attempt at a Solution

Applying the Euclidean Algorithm, I have

a = 6x

^{6}+ 12x

^{5}- 6x

^{4}-12x +12 = (3x

^{4}- 3)(2x

^{2}+ 4x -2) + (6x

^{2}+ 6)

b = 3x

^{4}- 3 = (6x

^{2}+ 6)(##\frac {1}{2}##x

^{2}- ##\frac {1}{2}##)

Now a monic polynomial has a leading coefficient of degree 1. Here, we have a common divisor of 6x

^{2}+ 6 which is not monic. How would I go about finding the monic greatest common divisor.

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