Question

Use long division to divide. (5 + 3x^2 + x^4) ÷ (3 − 2x + x^2)?

Answer 1

To divide (5 + 3x^2 + x^4) ÷ (3 - 2x + x^2) using long division, arrange the terms in descending order of their exponents and follow the steps of long division to find the quotient and remainder.

Step-by-step explanation:

To divide (5 + 3x^2 + x^4) ÷ (3 - 2x + x^2) using long division, follow these steps:

1. Arrange the terms in descending order of their exponents: x^4 + 3x^2 + 5.
2. Divide the first term of the numerator (x^4) by the first term of the denominator (x^2) and write the result (x^2) above the division line.
3. Multiply the entire denominator (3 - 2x + x^2) by the result (x^2) and write the product (3x^2 - 2x^3 + x^4) below the numerator.
4. Subtract the product from the numerator: (x^4 + 3x^2 + 5) - (3x^2 - 2x^3 + x^4).
5. Bring down the next term of the numerator (0) and repeat steps 2-4 until there are no more terms to bring down.
6. The final result is the quotient: x^2 + 3 + (remainder)/(divisor).