If two zeroes of the polynomial x⁴ - 6x³ - 26x² + 138x - 35 are 2 ± √3, find the other zeroes.

The two zeroes of the polynomial are 2 + √3, 2 - √3.
Therefore, (x - (2 + √3))(x - (2 - √3)) = x² + 4 - 4x - 3 = x² - 4x + 1 is a factor of the given polynomial.
Using division algorithm, we get
x⁴ - 6x³ - 26x² + 138x - 35 = (x² - 4x + 1)(x² - 2x - 35)
So, (x² - 2x - 35) is also a factor of the given polynomial.
x² - 2x - 35 = x² - 7x + 5x - 35 = x(x - 7) + 5(x - 7) = (x - 7)(x + 5)
Hence, 7 and -5 are the other zeros of this polynomial.