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Factor Theorem

x-2 is a fact...

Question

x - 2 is a factor of $x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 9$

True

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False

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Solution

The correct option is B
False

$x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 9$

x - 2 = 0

x = 2

Put x = 2 in the given expression

$(2)^{4} - 2 (2)^{3} + 5 (2)^{2} - 4 (2) + 9$

= 16 - 16 + 20 - 8 + 9

= 21, which is not equal to zero

$∴$ (x - 2) is not a factor of the given polynomial. Hence, the above statement is false.

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(x + 2) is a factor of 2x³ + 5x² - x - k. The value of k is:

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