Question

a) which of these are not potential rational roots of (8x^3 + 15x^2 - 7x - 5)? (pm \frac{1}{2}) (pm \frac{5}{8}) (pm 8) (pm \frac{1}{4}) (pm 5) (pm 1) (pm \frac{5}{2}) (pm \frac{1}{8}) (pm \frac{5}{4}) (pm 2) (pm \frac{5}{1}) (pm \frac{1}{1}) b) list all the potential rational roots of (2x^6 - 7x^4 - 6x^3 + 18x^2 - 1).

Explanation:

Step1: Recall Rational Root Theorem

Potential rational roots are $\pm\frac{\text{factors of constant term}}{\text{factors of leading coefficient}}$

Step2: Identify coefficients

For $8x^3 + 15x^2 -7x -5$, constant term $=-5$, leading coefficient $=8$.

Step3: List factors

Factors of 5: $\pm1, \pm5$; Factors of 8: $\pm1, \pm2, \pm4, \pm8$.

Step4: Generate all potential roots

$\pm1, \pm5, \pm\frac{1}{2}, \pm\frac{5}{2}, \pm\frac{1}{4}, \pm\frac{5}{4}, \pm\frac{1}{8}, \pm\frac{5}{8}$

Step5: Match against options

Compare each option to the generated list. $\pm8$ is not in the list.

Answer:

$\pm8$