Question

What are the possible rational zeros of f(x) = 3x3 - 4x2 - 7x + 21 ?

Answer 1

The rational root test... This involves finding all possible factors of the constant, and all possible factors of the leading coefficient \(\large(3x^3)\)

Answer 2

The constant is 21... what are the factors of 21?

Answer 3

1, 3, 7,21

Answer 4

That's good :)
Now what about the factors of 3, the leading coefficient?

Answer 5

1 3

Answer 6

Okay, great :)
Now, as per the "Rational Root Test"
the possible rational roots would be all possible numbers of the form
\[\Large \pm \frac{p}q\]
Where p is a factor of the constant (21) and q is a factor of the leading coefficient (3)

Just list them all out and exhaust the list :D

Answer 7

\[\pm1\pm3\pm7\pm21\]

Answer 8

What about \[\Large \pm \frac73\]?

Answer 9

ok I understand now!! Thank You!!