Value of a for Divisibility

Given Polynomial:
2x^4 - 9x^3 + 4x^2x + 1

Divisor Polynomial:
1 - 2x

Explanation:

1. To determine the value of 'a' for which the given polynomial is divisible by the divisor polynomial, we need to perform polynomial division.

2. Perform polynomial division of the given polynomial by the divisor polynomial:
(2x^4 - 9x^3 + 4x^2x + 1) ÷ (1 - 2x)

3. The result of the division should be a polynomial with a remainder of 0 for the given polynomial to be divisible by the divisor polynomial.

4. Solve the division and equate the remainder to 0 to find the value of 'a'.

5. By performing the division and setting the remainder to 0, we can find the value of 'a' for which the given polynomial is divisible by the divisor polynomial.

6. Once you find the value of 'a' that satisfies the divisibility condition, you have successfully determined the value of 'a' for which the given polynomial is divisible by 1 - 2x.