Question

Use long division to find the quotient and remainder.
(6x^4 + x^3 - 5x + 177) ÷ (x^2 + 6)

Answer 1

To divide (6x^4 + x^3 - 5x + 177) by (x^2 + 6) using long division, follow these steps: Start by dividing the first term of the numerator, 6x^4, by the first term of the denominator, x^2.

Step-by-step explanation:

To divide (6x^4 + x^3 - 5x + 177) by (x^2 + 6) using long division, follow these steps:

1. Start by dividing the first term of the numerator, 6x^4, by the first term of the denominator, x^2.
2. This gives us a quotient of 6x^2. Multiply the entire denominator, x^2 + 6, by this quotient, and subtract the result from the numerator.
3. Repeat this process for each term of the numerator, dividing it by the first term of the denominator and subtracting the result from the numerator.
4. The final result is the quotient, which is 6x^2 + x - 6, and the remainder, which is 183.