Answer :
Final answer:
The process of finding a remainder when dividing two polynomials involves using either polynomial or synthetic division techniques. Here, we've used synthetic division to simplify it. The remainder is the last number obtained in the subtraction step of the process.
Explanation:
To find the remainder when the polynomial 3x^4 - 6x^3 - 2x^2 + 19 is divided by the polynomial (x - 2), we can use polynomial division or synthetic division technique.
Let's use the synthetic division.
- Set up the division.
- Bring down the leading coefficient of the polynomial.
- Multiply the number brought down by the divisor's root and write the product underneath the next coefficient
- Add/subtract vertically and bring the resulting number down.
- Repeat step 3 and 4 until all coefficients have been used.
The last number resulting from the subtraction step gives you the remainder when the initial polynomial is divided by the divisor.
Learn more about Polynomial Division here:
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