Question

Divide using long division (3x⁴-4x³+12x²+5)-:(x²+1)

Answer 1

To divide using long division, you need to divide the first term of the numerator by the first term of the denominator and then subtract the result from the numerator. Repeat this process until the degree of the remainder is less than the degree of the denominator. The result of the division is the quotient and the remainder.

Step-by-step explanation:

To divide using long division, we need to follow these steps:

1. Divide the first term of the numerator by the first term of the denominator. In this case, divide 3x^4 by x^2, which gives us 3x^2.
2. Multiply the whole denominator (x^2+1) by the quotient obtained in the previous step. In this case, multiply (x^2+1) by 3x^2, which gives us 3x^4+3x^2.
3. Subtract the result obtained in the previous step from the numerator (3x^4-4x^3+12x^2+5) to get the remainder. In this case, subtract 3x^4+3x^2 from 3x^4-4x^3+12x^2+5. The remainder is -4x^3+9x^2+5.
4. Repeat steps 1-3 for the remainder until the degree of the remainder is less than the degree of the denominator.

Therefore, the result of the division (3x⁴-4x³+12x²+5) ÷ (x²+1) is 3x^2 with a remainder of -4x^3+9x^2+5.