Question

How to factor y^3 +2y^2 + 2y + 1

Answer 1

Explanation:

P(y) = y³ + 2y² + 2y + 1

P(-1) = (-1)³ + 2*(-1)² + 2*(-1) + 1

= -1 + 2 - 2 + 1

= 0

As, P(-1) = 0, (y + 1) is a factor.

Use synthetic division or remainder theorem.

-1 1 2 2 1

0 -1 -1 -1

1 1 1 0

quotient = y² + y + 1

y³ + 2y² + 2y + 1 = ( y + 1) (y² + y + 1)