Question

How to divide polynomials in fractions using long division

Answer 1

To divide polynomials in fractions using long division, follow these steps.

Step-by-step explanation:

To divide polynomials in fractions using long division, follow these steps:

1. Arrange the dividend and the divisor in long division format, placing the polynomial with the highest degree inside the division symbol and the one with the lower degree outside.
2. Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient.
3. Multiply the entire divisor by the first term of the quotient and subtract it from the dividend. Bring down the next term of the dividend.
4. Repeat steps 2 and 3 until the dividend is fully divided or until a remainder is obtained.

For example, if we have the polynomial (x^3 + 3x^2 + 2x + 1) divided by (x + 2), the first step would be to divide the first term of the dividend (x^3) by the first term of the divisor (x). This gives us the first term of the quotient as (x^2). We then multiply (x + 2) by (x^2) and subtract it from the dividend (x^3 + 3x^2 + 2x + 1 - (x^3 + 2x^2)). This leaves us with (x + 2) as the updated dividend. We repeat the process until the dividend is fully divided or until we obtain a remainder.