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The problem states that (x-2) is a factor. According to the Factor Theorem, if (x-2) is a factor, then P(2) must be 0.

Mathematics

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The polynomial given is 2x3−x−8x+42x^3 - x - 8x + 4, which simplifies to 2x3−9x+42x^3 - 9x + 4.
Let P(x)=2x3−9x+4P(x) = 2x^3 - 9x + 4.
The problem states that (x−2)(x-2) is a factor. According to the Factor Theorem, if (x−2)(x-2) is a factor, then P(2)P(2) must be 0.
Let's check P(2)P(2):

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