Question

Use synthetic division to evaluate the function f(x)=x^ + 3x - x² + 2x - 6 for f(3),

Answer 1

The question relates to the evaluation of a polynomial function at a specific value using synthetic division. The function contains a typo and after correcting it, the process of synthetic division is explained step-by-step to find f(3).

Step-by-step explanation:

The student's question involves evaluating a polynomial function at a given value using synthetic division. However, there seems to be a typo in the function provided, as it is not written in standard polynomial order and contains additional symbols. Assuming the correct function is f(x) = x3 + 3x2 - x + 2 - 6 and we want to find f(3), we will proceed with synthetic division.

Here are the steps for synthetic division:

1. Write down the coefficients of the polynomial in decreasing order of the degree, which would be 1 (for x3), 3 (for 3x2), -1 (for -x), and -4 (for 2-6).
2. Write the value we are evaluating the function at, which is 3, to the left of the coefficients.
3. Bring down the first coefficient (1) to the bottom row.
4. Multiply this coefficient by 3 and write the result under the next coefficient.
5. Add the numbers in this column and write the sum in the bottom row. Repeat this process for the rest of the coefficients.
6. The last number in the bottom row is the value of f(3).

The process of synthetic division yields the value of the function at x=3 without the need for long division or substituting the value into the polynomial.