Question

If 3 and –3 are two zeroes of the polynomial (x⁴ + x³ – 11x² – 9x + 18), find all the zeroes of the given polynomial.

Answer 1

Let x⁴ + x³ – 11x² – 9x + 18 

Since 3 and – 3 are the zeroes of f(x), it follows that each one of (x + 3) and (x – 3) is a factor of f(x). 

Consequently, (x – 3) (x + 3) = (x² – 9) is a factor of f(x). 

On dividing f(x) by (x² – 9), we get: