Question

Factorise y³ + y² – y – 1

Answer 1

Let f(y) = y³ + y² – y – 1 

f(1) = 1³ + 1² – 1 – 1 = 0 

(y – 1) is a factor of f(y).

Now dividing f(y) by (y – 1)

∴ f(x) = (x + 1)(x² + 12x + 20) 

But (x² + 12x + 20) = x² + 10x + 2x + 20 

=x(x + 10)+2(x + 10) 

=(x + 10)(x + 2) 

∴f(x) = (x + 1)(x + 2)(x + 10)