How do you divide the expression (3x^3 + 2x^2 + x + 2) by (x^2)?

Dividing the Expression by x²

To divide the expression (3x³ + 2x² + x + 2) by (x²), we will break the division down and simplify it term by term.

Step-by-Step Process

1. Start with the expression: 3x³ + 2x² + x + 2.
2. Separate the expression by dividing each term by x²:
3. • 3x³ ÷ x² = 3x (since x³ divided by x² equals x raised to the power of 1)
   • 2x² ÷ x² = 2 (the x² cancels out)
   • x ÷ x² = 1/x (since there is one x on the bottom)
   • 2 ÷ x² = 2/x² (keep the x² in the denominator)

Final Result

After dividing each term, we combine the results:

The result of the division is:

3x + 2 + 1/x + 2/x²

Conclusion

Thus, when you divide the expression (3x³ + 2x² + x + 2) by (x²), you obtain:

3x + 2 + 1/x + 2/x²