The correct option is (2)
and (3)
.
The factor of equation f(x) = 60
+ 86
– 46
– 43
+ 8 are
and
.
<h3>Rational Root Theorem: </h3>
The rational root theorem, also referred to as the rational zero theorem, is a potent mathematical technique used to identify all potential rational roots of polynomial equations of order 3 and above.
For the given polynomial, the roots are given as;
![$$P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}$$\\ \\$\pm \frac{\text { factors of } a_{0}}{\text { factors of } a_{n}}$.](https://tex.z-dn.net/?f=%24%24P%28x%29%3Da_%7Bn%7D%20x%5E%7Bn%7D%2Ba_%7Bn-1%7D%20x%5E%7Bn-1%7D%2B%5Ccdots%2Ba_%7B2%7D%20x%5E%7B2%7D%2Ba_%7B1%7D%20x%2Ba_%7B0%7D%24%24%5C%5C%20%5C%5C%24%5Cpm%20%5Cfrac%7B%5Ctext%20%7B%20factors%20of%20%7D%20a_%7B0%7D%7D%7B%5Ctext%20%7B%20factors%20of%20%7D%20a_%7Bn%7D%7D%24.)
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.
Out of the given options, only
and
can be written in the form:
![\begin{aligned}&\frac{8}{5}=\frac{\text { a factor of } 8}{\text { a factor of } 60} \\&\frac{1}{6}=\frac{\text { a factor of } 8}{\text { a factor of } 60}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26%5Cfrac%7B8%7D%7B5%7D%3D%5Cfrac%7B%5Ctext%20%7B%20a%20factor%20of%20%7D%208%7D%7B%5Ctext%20%7B%20a%20factor%20of%20%7D%2060%7D%20%5C%5C%26%5Cfrac%7B1%7D%7B6%7D%3D%5Cfrac%7B%5Ctext%20%7B%20a%20factor%20of%20%7D%208%7D%7B%5Ctext%20%7B%20a%20factor%20of%20%7D%2060%7D%5Cend%7Baligned%7D)
Therefore, the rational roots of polynomial f(x) = 60
+ 86
– 46
– 43
+ 8 are
and
.
To know more about Rational Root Theorem, here
brainly.com/question/10937559
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The complete question is-
Which is a factor of f(x) = 60
+ 86
– 46
– 43
+ 8? use the rational root theorem to help you find your answer.
- x – 6 => 6
- 5x – 8 =>
- 6x – 1 =>
![\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D)
- 8x + 5 =>
![\frac{-5}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B-5%7D%7B8%7D)