Question

(1-x^2-3x+6x^3) : (2x-1)

Answer 1

Полное решение, пожалуйста!

Answer 2

To divide the polynomial (1 - x^2 - 3x + 6x^3) by (2x - 1), we can use polynomial long division. Here's the step-by-step process:

Step 1: Arrange the terms of both polynomials in descending order of exponents. Step 2: Divide the first term of the dividend (dividend is the polynomial being divided) by the first term of the divisor (divisor is the polynomial we're dividing by). This gives us the first term of the quotient. Step 3: Multiply the divisor by the first term of the quotient and subtract it from the dividend. Step 4: Repeat steps 2 and 3 with the result of the previous subtraction until the degree of the remainder is less than the degree of the divisor.

Now, let's perform the polynomial long division:

scssCopy code
            3x^2 + 2x + 1
         _____________________
2x - 1 | 6x^3 - x^2 - 3x + 1
        - (6x^3 - 3x^2)
         _______________
                     2x^2 - 3x
          - (2x^2 - x)
         _______________
                               -2x + 1
             - (-2x + 1)
         _______________
                                0

The result of the division is: 3x^2 + 2x + 1. The remainder is 0, which means the division is exact, and there is no remainder.