Question

If (y – 3) is a factor of y³ – 2y² – 9y + 18, then find the other two factors.

Answer 1

Let f(y) = y³ – 2y² – 9y + 18 

Given that (y – 3) is a factor of f(y). 

Dividing f(y) by (y – 3)

∴ f(y) = (y – 3) (y + y – 6) 

But y² + y – 6 

= y² + 3y – 2y – 6 

= y (y + 3) – 2 (y + 3) 

= (y + 3) (y – 2) 

∴ f(y) = (y – 2)(y – 3)(y + 3) 

The other two factors are (y – 2) and (y + 3)