(x^2+x+1)(x^2+x+2)-6

Jasonbradley

less than a minute read

·

Jun 17, 2024

20

Share

Factoring the Expression (x^2 + x + 1)(x^2 + x + 2) - 6

This article will guide you through the process of factoring the expression:

(x² + x + 1)(x² + x + 2) - 6

Let's break down the steps:

1. Substitution

To simplify the expression, we can introduce a substitution:

Let y = x² + x

Now our expression becomes:

(y + 1)(y + 2) - 6

2. Expanding the Expression

Now we can expand the brackets:

• y² + 2y + y + 2 - 6

Simplifying, we get:

• y² + 3y - 4

3. Factoring the Quadratic Expression

The expression is now a simple quadratic equation. We can factor it as:

• (y + 4)(y - 1)

4. Substituting Back

Finally, we substitute back our original value for y:

• (x² + x + 4)(x² + x - 1)

Conclusion

Therefore, the factored form of the expression (x² + x + 1)(x² + x + 2) - 6 is (x² + x + 4)(x² + x - 1).