Question

MAKING AN ARGUMENT You use synthetic division to divide f(x) by (x − a) and find that the remainder equals 15. Your friend concludes that f (15) = a. Is your friend correct? Explain your reasoning.

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No, your friend is not correct. The remainder obtained from synthetic division when dividing f(x) by (x-a) does not give us any information about the value of f(15) equaling a.

Synthetic division is used to divide a polynomial function f(x) by a linear factor (x-a). The remainder obtained is the value of f(a). In this case, the remainder is given as 15 which means that f(a) equals 15, not f(15) equals a.

To summarize:

Your friend's conclusion: f(15) = a

Correct conclusion: f(a) = 15

Answer: No, your friend is not correct. The remainder obtained from synthetic division does not provide information about the value of f(15) equaling a.

Synthetic division is used to divide a polynomial function f(x) by a linear factor (x-a). The remainder obtained is the value of f(a). In this case, the remainder is given as 15 which means that f(a) equals 15, not f(15) equals a.

To summarize:

Your friend's conclusion: f(15) = a

Correct conclusion: f(a) = 15

Answer: No, your friend is not correct. The remainder obtained from synthetic division does not provide information about the value of f(15) equaling a.

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