To divide the polynomial 3x² + 11x + 4 by x², we can use polynomial long division.
1. Begin by writing the expression: (3x² + 11x + 4) ÷ x².
2. Divide the first term of the numerator (3x²) by the first term of the denominator (x²). This gives us 3.
3. Multiply 3 by the entire divisor x², resulting in 3x².
4. Subtract this result from the original polynomial:
(3x² + 11x + 4) – 3x² = 11x + 4.
5. Now, we divide the next term, 11x, by x². Since 11x cannot be divided by x² evenly, we keep the remainder.
6. The final expression from the division is 3 + (11x + 4)/x².
In conclusion, the result of dividing 3x² + 11x + 4 by x² is:
3 + (11x + 4)/x²