Question

How to use synthetic division to evaluate a function?

Answer 1

To use synthetic division to evaluate a function, follow these steps: arrange the function in descending order, divide coefficients by the divisor,., and the remainder is the final result.

Step-by-step explanation:

To use synthetic division to evaluate a function, you need to follow these steps:

1. Arrange the function in descending order of powers.
2. Divide the coefficients of each term in the function by the divisor.
3. Bring down the leading coefficient.
4. Multiply the divisor by the quotient from the previous step.
5. Subtract the result from the previous step from the coefficients of the next higher power term.
6. Repeat steps 3-5 until you have gone through all the terms.
7. The final result will be the remainder after the last step, and the coefficients of the quotient.

For example, let's say we want to evaluate the function f(x) = 2x^3 + 5x^2 - 3x + 1, at x = 2. We can use synthetic division as follows:

2 | 2 5 -3 1

-4 2 -2 -2

2 1 -1 -1

So the result is the quotient: 2x^2 + x - 1, and the remainder: -1.