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Is x-3 a factor of x- 9x² - 14x + 24?

User Santina
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1 Answer

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9514 1404 393

Answer:

no

Explanation:

We assume you are concerned with the cubic

x³ -9x² -14x +24

Its factors are all irrational, as shown in the attached graph. x-3 is not a factor.

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x-3 is a factor if the expression evaluates to zero when x=3. Here, it does not.

((x -9)x -14)x +24 for x=3 is ...

((3 -9)(3) -14)(3) +24 = (-18 -14)(3) +24 = -96 +24 = -72

The remainder from division by x-3 is not zero, so x-3 is not a factor.

User Swizec Teller
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