Question

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

• A. 5
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A 5

Let the zeros of the polynomial be a, b and c. Then,
$p\left(x\right)=(x-a)(x-b)(x-c)$

The constant term of the polynomial is $abc=24$.
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.