Answer :
Final answer:
The division of the polynomial (12x³ + 19x²-15x-21) by (4x² + 5x) involves polynomial long division, a method similar to elementary long division, but uses polynomials and subtracts exponents when dividing terms.
Explanation:
The original problem is polynomial long division of (12x³+19x²-15x-21) by (4x²+5x). In polynomial long division, you start by checking how many times the first term of the divisor (4x²) fits into the first term of the dividend (12x³). Then you multiply the result by the divisor and subtract it from the original polynomial, then bring down the next term.
Following this process, the result of dividing 12x³ by 4x² equals 3x. You then multiply the divisor (4x²+5x) by this result and subtract it from the original polynomial, yielding the intermediate result. Repeat this process to find each term of the quotient until you can't divide anymore.
Please note that this process is similar to the long division you learned in elementary school, but instead of working with decimal numbers, you're working with polynomials where you also subtract the exponents when dividing terms.
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