Obtain all other zeroes of 3x⁴ + 6x³ – 2x² – 10x – 5, if two of its zeroes are and .

p(x) = 3x⁴ + 6x³ – 2x² – 10x – 5

Since the two zeroes are

is a factor of 3x⁴ + 6x³ – 2x² – 10x – 5

Therefore, we divide the given polynomial by

We know,
Dividend = (Divisor × quotient) + remainder

3 x⁴ + 6 x³ – 2x² – 10 x – 5

3 x⁴ + 6 x³ – 2 x² – 10 x – 5
As (a + b)² = a² + b² + 2ab

3 x⁴ + 6 x³ – 2 x² – 10 x – 5 = 3 (x + 1)²

Therefore, its zero is given by x + 1 = 0, x = −1

Hence, the zeroes of the given polynomial are and – 1, –1.