It is given that the polynomial $p (x) = x^{3} - 9 x^{2} + 26 x + 24$ has zeroes that are integers. Which of the following is not a zero of the polynomial.

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Solution

The correct option is A 5
Let the zeros of the polynomial be a, b and c. Then,
$p (x) = (x - a) (x - b) (x - c)$

The constant term of the polynomial is $a b c = 24$ .
Also, it is given that a, b and c, all are integers.
So, the zeroes of the polynomial are factors of 24. Possible zeroes are:
$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12, \pm 24$

Clearly, $5$ is not a zero of the polynomial.

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