Final answer:
Dividing the polynomial (4x^4+0.4x^2−3x+0.8) by the polynomial (x^2−x−1) using long division, quotient obtained will be 4x^2+4x+1, and the remainder will be 4x−1.
Step-by-step explanation:
To divide the polynomial (4x^4+0.4x^2−3x+0.8) by the polynomial (x^2−x−1) using long division, follow these steps:
1. Divide the first term of the dividend by the first term of the divisor.
In this case, (4x^4) ÷ (x^2) = 4x^2.
2. Multiply the divisor by the quotient obtained in step 1.
In this case, (x^2−x−1) × (4x^2) = 4x^4−4x^3−4x^2.
3. Subtract the result obtained in step 2 from the dividend.
In this case, (4x^4+0.4x^2−3x+0.8) − (4x^4−4x^3−4x^2) = 4x^3+4.4x^2−3x+0.8.
4. Repeat steps 1-3 with the new dividend obtained in step 3.
5. Continue this process until the degree of the new dividend is less than the degree of the divisor.
The final quotient obtained from this long division will be 4x^2+4x+1, and the remainder will be 4x−1.
Therefore, (4x^4+0.4x^2−3x+0.8) ÷ (x^2−x−1) = 4x^2+4x+1 with a remainder of 4x−1.