Question

If h(w) = 14w? - 33w - 23, use synthetic division to find h(3).

A) 10
B) -10
C) 5
D) -5

Answer 1

Using synthetic division to find h(3) for the polynomial h(w) = 14w^2 - 33w - 23, we determine the result is 4, which is not listed in the provided options.

Step-by-step explanation:

To find h(3) using synthetic division for the given polynomial h(w) = 14w2 - 33w - 23, we set up the synthetic division with 3 as the root we are testing.

1. Write down the coefficients of the polynomial: 14, -33, -23.
2. Bring down the leading coefficient (14) to the bottom row.
3. Multiply the initial value by 3 (the root) and write the result under the next coefficient.
4. Add the results in the second column and multiply again by 3, repeating this process until all coefficients have been used.

The last value in the bottom row will give us the result of h(3).

• 14 (Bring down)
• 14 * 3 = 42 (Write under -33)
• -33 + 42 = 9 (Write down)
• 9 * 3 = 27 (Write under -23)
• -23 + 27 = 4 (Result for h(3))

Therefore, h(3) equals 4, which is not one of the provided options, indicating a possible mistake in the question or options given.