Question

Use the long division method to find the result when 12x³+19x²+24x+5 is divided by 4x+1.

Answer 1

To divide 12x³+19x²+24x+5 by 4x+1 using long division, follow the steps of arranging, dividing, subtracting, and bringing down the terms until the division is complete. The result is 3x²+4x+1.

Step-by-step explanation:

To divide 12x³+19x²+24x+5 by 4x+1 using long division, follow these steps:

1. Arrange the dividend and divisor in descending order of their exponents. It becomes 12x³+19x²+24x+5 divided by 4x+1.
2. Divide the first term in the dividend (12x³) by the first term in the divisor (4x). The quotient is 3x².
3. Multiply the divisor (4x+1) by the quotient (3x²) and subtract it from the dividend.
4. Bring down the next term (24x) and repeat steps 2 and 3 until all terms have been divided.

The result of dividing 12x³+19x²+24x+5 by 4x+1 is 3x²+4x+1.