Question

Which of these are NOT potential rational roots of 8x^3 + 15x^2 – 7x – 5?

Answer 1

The numbers that are not potential rational roots of the polynomial function, are numbers other than any of $\pm 1, \pm \frac 12,\pm \frac 14,\pm \frac 18,\pm 5, \pm \frac 52, \pm \frac 54, \pm \frac 58$

The polynomial function is given as:

$g(x) = 8x^3 + 15x^2 - 7x -5$

How to calculate the potential rational roots

The potential rational roots of a polynomial function g(x).

Such that: $g(x) = px^n + ....+q$

is:

$Roots = \pm \frac{Factors\ of\ q}{Factors\ of\ p}$

So, we start by listing out the factors of 5 and 8

$5 =1 ,5$

$8 =1 ,2,4,8$

$Roots = \pm \frac{Factors\ of\ q}{Factors\ of\ p}$ becomes

$Roots = \pm \frac{1,5}{1,2,4,8}$

Simplify

$Roots = \pm 1, \pm \frac 12,\pm \frac 14,\pm \frac 18,\pm 5, \pm \frac 52, \pm \frac 54, \pm \frac 58$

Hence, the numbers that are not potential rational roots of the polynomial function, are numbers other than any of $\pm 1, \pm \frac 12,\pm \frac 14,\pm \frac 18,\pm 5, \pm \frac 52, \pm \frac 54, \pm \frac 58$

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