To find the quotient when the polynomial 5x³ + 3x² + 3x + 8 is divided by x³, we can use polynomial long division.
1. Start by dividing the leading term of the dividend (5x³) by the leading term of the divisor (x³). The result is 5.
2. Multiply the entire divisor (x³) by 5, which gives us 5x³.
3. Subtract 5x³ from the original polynomial:
(5x³ + 3x² + 3x + 8) – (5x³) = 3x² + 3x + 8
4. Now, we take the next term down. Dividing the leading term of what’s left (3x²) by x³ gives us 0 since the degree of 3x² is less than the degree of x³.
5. This means we cannot divide any further. Therefore, the quotient of the division is 5 and the remainder is 3x² + 3x + 8.
In conclusion, the quotient when 5x³ + 3x² + 3x + 8 is divided by x³ is 5.