Question

Use the long division method to find the result when 3x³+29x²+30x+8 divided by 3x+2.

Answer 1

Using long division, the polynomial 3x³ + 29x² + 30x + 8 divided by 3x + 2 results in a quotient of x² + 9x + 6 with no remainder.

Step-by-step explanation:

To divide the polynomial 3x³+29x²+30x+8 by 3x+2 using the long division method, we follow these steps:

1. Divide the first term of the numerator by the first term of the denominator: 3x³ ÷ 3x equals x².
2. Multiply the entire divisor 3x+2 by x² and subtract the result from the numerator.
3. Bring down the next term from the numerator to form a new sub-polynomial and repeat the process until all terms are accounted for.

The result of this division is a polynomial and, possibly, a remainder. For the given polynomials, after performing the long division, we find that the final quotient is x² + 9x + 6 and the remainder is 0, so there is no remainder term.

The quotient of 3x³ + 29x² + 30x + 8 divided by 3x + 2 is x² + 9x + 6. There is no remainder.