Question

Divide 3x^3-2x^2+3x+2 by x + 4

Answer 1

To divide 3x^3-2x^2+3x+2 by x + 4, you can use polynomial long division. The quotient is 3x^2 - 14 and the remainder is 59x + 238. Therefore, the division is equal to 3x^2 - 14 + (59x + 238) / (x + 4).

Step-by-step explanation:

To divide 3x^3-2x^2+3x+2 by x + 4, we can use polynomial long division. Here are the steps:

1. Start by dividing the highest degree term, 3x^3, by x. The result is 3x^2.
2. Multiply the divisor, x + 4, by the quotient term, 3x^2, to get 3x^3 + 12x^2.
3. Subtract 3x^3 + 12x^2 from 3x^3-2x^2+3x+2 to get -14x^2+3x+2.
4. Repeat the process by dividing the new polynomial, -14x^2+3x+2, by x.
5. Continue the division until the degree of the remainder is less than the degree of the divisor.

Using polynomial long division, the quotient is 3x^2 - 14 and the remainder is 59x + 238. Therefore, the division is equal to 3x^2 - 14 + (59x + 238) / (x + 4).