Question

Find the quotient and remainder. {2x⁴+3x³-12}{x+4}

Answer 1

To determine the quotient and remainder of the division of the polynomial 2x⁴ + 3x³ - 12 by x + 4, polynomial long division must be used, systematically dividing and subtracting until reaching the final terms.

Step-by-step explanation:

To find the quotient and remainder of the polynomial 2x⁴ + 3x³ - 12 when divided by x + 4, we use polynomial long division.

1. Divide the first term of the numerator by the first term of the denominator: 2x⁴ ÷ x = 2x³.
2. Multiply x + 4 by 2x³ and subtract the result from 2x⁴ + 3x³.
3. Bring down the next term of the numerator and repeat the process until you cannot divide anymore.

Ultimately, this process will give you the quotient and the remainder, if there is any, of the division.