Question

Evaluate the polynomial function 2x³ - 3x² + 4x + 2 for x = 4 using synthetic substitution.

Answer 1

To evaluate the polynomial 2x³ - 3x² + 4x + 2 at x = 4 using synthetic substitution, we systematically combine the coefficients with the value of x through multiplication and addition to arrive at the final value, which is 98.

Step-by-step explanation:

To evaluate the polynomial function 2x³ - 3x² + 4x + 2 for x = 4 using synthetic substitution, we follow these steps:

1. Write down the coefficients of the polynomial: 2, -3, 4, 2.
2. Write the value of x for synthetic substitution (here x = 4) to the left of the coefficients.
3. Bring down the first coefficient (2).
4. Multiply this number by x (our synthetic x-value, which is 4 in this case) and write the result under the second coefficient -3. Add these two values to get the next coefficient in the next row.
5. Repeat this process for all coefficients.
6. The last number obtained in the row will be the value of the polynomial for x = 4.

By applying these steps, we get the following:

• 2 (the first coefficient is brought down)
• 2 * 4 = 8, and -3 + 8 = 5
• 5 * 4 = 20, and 4 + 20 = 24
• 24 * 4 = 96, and 2 + 96 = 98 (this is the value of the polynomial for x = 4)

So, the evaluation of 2x³ - 3x² + 4x + 2 for x = 4 is 98.