How do you factor 2y³+y²-2y-1?

To factor the expression \(2y^3 + y^2 - 2y - 1\), we can start by grouping the terms. This method helps us find common factors within parts of the polynomial.

Step 1: Group the Terms

We can group the polynomial as follows:

• (2y³ + y²)
• (-2y - 1)

Step 2: Factor Each Group

Now, let's factor out the common factors from each group:

• From the first group, \(y²(2y + 1)\)
• From the second group, \(-1(2y + 1)\)

Step 3: Combine the Factors

Now we can combine these factored groups:

We have:

y²(2y + 1) - 1(2y + 1)

This can be rewritten as:

(2y + 1)(y² - 1)

Step 4: Factor Further

The term \(y² - 1\) is a difference of squares, which can be factored as:

(y - 1)(y + 1)

Final Factored Form

Putting it all together, the complete factorization of the original expression is:

(2y + 1)(y - 1)(y + 1)

This is the fully factored form of the polynomial \(2y³ + y² - 2y - 1\).