Answer:
Step-by-step explanation:
Given is an algebraic polynomial of degree 5.
[tex]g(x) = 3x^5-2x^4+9x^3-x^2+12\\[/tex]
Here leading term is p=3 and constant term is q =12
Factors of p are ±1,±2,±3
Factors of q are [tex]\frac{±1,±2,±3,±4,±6,±12} \\[/tex]
Possible forms of p/q will be the same for any other polynomial of degree 5 with leading term =3 and constant term = 12
Hence any other polynomial
[tex]g(x) = 3x^5+ax^4+bx^3+cx^2+12[/tex]
will have same possible zeroes of p/q, when a,b,c are rational.
Hence any polynomial of this type would have the same possible rational roots.
The answer is A, or [tex]f(x) = 3x^{5} - 2x^{4} - 9x^{3} + x^{2} - 12[/tex]
If the picture won't load, the correct equation is f(x) = 3x^5 – 2x^4 – 9x^3 + x^2 – 12
Just got it right on the quiz, hope this helps!! :)
