Question

Use synthetic division and the Remainder Theo f(x)=x^(4)+3x^(3)+5x^(2)-7x-6;f(6)

Answer 1

To evaluate the polynomial function f(x) = x^4 + 3x^3 + 5x^2 - 7x - 6 at f(6), synthetic division and the Remainder Theorem can be applied, which involves a series of multiplication and addition steps using the coefficients of f(x) and the value 6.

Step-by-step explanation:

The question asks us to use synthetic division and the Remainder Theorem to evaluate the polynomial function f(x) = x^4 + 3x^3 + 5x^2 - 7x - 6 at f(6). The Remainder Theorem states that if a polynomial f(x) is divided by (x - k), the remainder is f(k). By applying synthetic division with 6, we perform the following steps:

1. Write down the coefficients of f(x): 1, 3, 5, -7, -6.
2. Bring down the first coefficient (1) as it is.
3. Multiply this by 6 (the value we are evaluating at) and write the result under the second coefficient.
4. Add the second coefficient and the value obtained from step 3. Continue this process across all coefficients.
5. The last number obtained is the remainder, which is f(6).

The result of these steps will give us the value of f(6), which also represents the remainder when f(x) is divided by (x - 6).