Which value is NOT a solution to the functionf(x)=x4−8x3+15x2+8x−16 ?

Question

Which value is NOT a solution to the functionf(x)=x4−8x3+15x2+8x−16 ?

BlackTom AI · Accepted Answer

First, I will restate the problem to ensure clarity: we are asked which value is NOT a solution to the function f(x) = x^4 − 8x^3 + 15x^2 + 8x − 16.

Next, I note that the provided answer options are missing in this case, so we don’t have a list of candidate values to evaluate one by one. This makes it impossible to identify which option among them is not a solution based on the options alone.

Nevertheless, we can independently test the specific value mentioned in the answer field, x = 2, to see whether it satisfies f(x) = 0. Evaluating the function at x = 2: f(2) = 2^4 − 8·(2^3) + 15·(2^2) + 8·2 − 16 = 16 − 64 + 60 + 16 − 16.

Performing the arithmetic step by step: 16 − 64 = −48, then −48 + 60 = 12, then 12 + 16 = 28, and finally 28 − 16 = 12. Therefore, f(2) = 12, which is not equal to 0.

From this calculation, we can conclude that x = 2 is not a root of the equation f(x) = 0; that is, 2 is not a solution to the function in the sense of solving f(x) = 0.

If, in a complete problem, there were multiple candidate values to test, the same procedure would apply: substitute each candidate into f(x) and check whether the result is zero. If the result is zero, that candidate is a solution; if not, it is not a solution.

A common misconception to avoid here is assuming that because a value seems related to the coefficients, it must be a root. Polynomial roots are determined by direct substitution or by factoring, not by intuition about coefficients alone.

In summary, given the lack of answer options, we can still verify that x = 2 is not a solution by direct evaluation, since f(2) = 12 ≠ 0.

ALGII141-027 4.8 Practice Problems

Which value is NOT a solution to the functionf(x)=x4−8x3+15x2+8x−16 ?

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