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Given f(x) = 3x - 14x³+3x²+18x + 23, use synthetic division to determine f(4).
f(4) =

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Final answer:

To use synthetic division to determine f(4), divide the polynomial by the binomial x - 4. The quotient obtained from the synthetic division will give the value of f(4), which is 3.

Step-by-step explanation:

To use synthetic division to determine f(4), we will divide the given polynomial f(x) = 3x - 14x³ + 3x² + 18x + 23 by the binomial x - 4 using synthetic division.

First, set up the division like this:

4 | -14 3 18 23

Next, bring down the coefficient of the first term, which is -14:

4 | -14 3 18 23 | -14

Multiply the divisor 4 by -14, and write the result under the next coefficient:

4 | -14 3 18 23 | -14 | -56

Add the first two terms of the dividend and write the sum below the line:

4 | -14 3 18 23 | -14 | -56 | 0

Multiply the divisor 4 by the new result, which is 0:

4 | -14 3 18 23 | -14 | -56 | 0 | 0

Add the next two terms of the dividend and write the sum below the line:

4 | -14 3 18 23 | -14 | -56 | 0 | 0 | 23

The quotient of the synthetic division is shown to be 3. Therefore, f(4) = 3.

User Manjeet Singh
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