Question

A polynomial function g(x) with integer coefficients has a leading coefficient of -8 and a constant term of –3. According to the Rational Root Theorem, which of the following are possible roots of g(x)?

Answer 1

The rational root theorem is used to determine the possible roots of a polynomial

The possible roots of g(x) are: $\pm 1, \pm \frac 12, \pm \frac 14, \pm \frac 18, \pm 3, \pm \frac 32, \pm \frac 34, \pm \frac 38$

The leading coefficient (p) is given as:

$p = -8$

The constant term (q) is given as:

$q= -3$

Using rational root theorem, the possible roots are:

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

The roots of p and q are:

$-8 = \pm 1, \pm 2, \pm 4, \pm 8$

$-3 = \pm 1, \pm 3$

So, we have:

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

Substitute known values

$Roots = \pm\frac{1,3}{1,2,4,8}$

Divide

$Roots = \pm 1, \pm \frac 12, \pm \frac 14, \pm \frac 18, \pm 3, \pm \frac 32, \pm \frac 34, \pm \frac 38$

Hence, the possible roots of g(x) are: $\pm 1, \pm \frac 12, \pm \frac 14, \pm \frac 18, \pm 3, \pm \frac 32, \pm \frac 34, \pm \frac 38$

Read more about rational root theorem at:

brainly.com/question/10937559