Question

Use synthetic substitution to find f(1) for the function f(x) = x^2 + 2x + 3.

A. 4

B. 7

C. 1

D. 9

Answer 1

Synthetic substitution using the value 1 for the polynomial f(x) = x² + 2x + 3 yields a result of 6, which is the value of f(1). However, this result does not match any of the provided options, suggesting an error in the question or options.

Step-by-step explanation:

To use synthetic substitution to find f(1) for the function f(x) = x² + 2x + 3, we set up the synthetic division table using 1 as the root we are testing.

1. Write down the coefficients of the polynomial: 1 (for x²), 2 (for x), and 3 (the constant term).
2. Bring down the first coefficient (1).
3. Multiply this coefficient by 1 and write the result under the next coefficient. Add the numbers in this column to find the new coefficient: 1 (first coefficient) * 1 = 1. The sum is 2 + 1 = 3.
4. Multiply the result by 1 again and add it to the next number in the row, which is the constant term: 3 * 1 = 3. Adding this to the constant term 3 gives us 6.

The last number obtained after applying synthetic division is the value of f(1). Therefore, f(1) = 6, which is not one of the options provided, indicating a possible misunderstanding of the question or the given options.

However, if we simply substitute 1 into the equation f(x) = x² + 2x + 3, we get: f(1) = 1² + 2(1) + 3 = 1 + 2 + 3 = 6.