use the rational zeros theorem to write a list of all potential rational zeros f(x) =13x3+23x2+2x-26

Question

mathstudent55 · Answer

a0 = -26 = p
a3 = 13 = q
List all factor of p and all factors of q.
The potential zeros are all x = p/q and x = -p/q

anonymous · Answer

what is a0 and a3 ?

mathstudent55 · Answer

$\large f(x) = a_nx^n + a_{n - 1}x^{n - 1} + ... + a_3x^3 + a_2x^2 + a_1x + a_0$

$a_3$ is the leading coefficient, the coefficient of the term of highest degree.
$a_0$ is the constant term, the term with no x.

mathstudent55 · Answer

Compare the general form above with what you have:

$f(x) = 13x^3+23x^2+2x-26$

That means that for you, $a_3 = 13$, and $a_0 = -26$.

mathstudent55 · Answer

Now find all the factors of $a_0 = -26$ and all the factors of $a_3 = 13$.

anonymous · Answer

so is it -/+1, -/+ 1/3, -/+ 2,-/+ 13, -/+ 26 ??

mathstudent55 · Answer

Keep the factors of the two numbers separate, because the factors of a0 go in the numerator, and the factors of a3 go in the denominator.
The factors of a0 = -26 are 1, 2, 13 
The factors or a3 = 13 are 1, 13
The possible zeros are all combinations of p/q, both positive and negative. Remember, p comes from the constant term,and q comes from the leading coefficient.

These are the possibilities:
1/1, 1/13, 2/1, 2/13, 13/1, 13/13
We can reduce to:
1, 1/13, 2, 2/13, 13, 1
Now eliminate repeats:
1, 1/13, 2, 2/13, 13

Now add the negatives:
1, -1, 1/13, -1/13, 2, -2, 2/13, -2/13, 13, -13