Question

According to the rational root theorem, which of the following are possible roots of the polynomial function below?

F(x) = 8x3 - 3x2 + 5x + 15
A. 5
B. 4
C. -1/4
D. -3
E. 5/2
F. 2/3

Answer 1

how do we use the rational roots thrm?

Answer 2

Not sure?

Answer 3

then you may want to read what the rational roots thrm is, give me a definition of it and lets see what part of it your not grasping.

Answer 4

The number by which it's all divided?

Answer 5

hmm, not quite.

my recollection of the rrt is that the only possible rational roots that a poly can have can be determined from a pool of options created from the factors of the constant term divided by the factors of coefficient of the highest degree in the poly.

Answer 6

the factors of your constant term: 15, are 1,3,5,15
the factors of highest degree term: 8, are 1,2,4,8

so the rrt says that if we are to have any rational root, it must be of the form:\[\pm\frac{1,3,5,15}{1,2,4,8}\]

Answer 7

now the question is, what can we form from these?

A. 5/1
B. 4/1
C. -1/4
D. -3/1
E. 5/2
F. 2/3

Answer 8

What do you mean by form?

Answer 9

pick a number from the top, and divide it by a number from the bottom. those are the only numbers we can use to form a fraction with

Answer 10

for instance:\[\frac{4}{7}\not \in\frac{1,3,5,15}{1,2,4,8}\]
since we cannot form 4/7 out of the given options

Answer 11

but 5/1 is an option since
\[\frac{5}{1} \in\frac{1,3,\color{red}5,15}{\color{red}1,2,4,8}\]

Answer 12

That would be the only one possible?

Answer 13

i see 2 that are not possible, and the rest are

Answer 14

see if you can make a stated option from the given pool of numbers

Answer 15

please help @amistre64

Answer 16

Would it be everything except B and F?

Answer 17

@amistre64