Question

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

f(x) = -2x^4 + 4x^3 + 3x^2 + 18

Answer 1

\[f(x) = -2x^4 + 4x^3 + 3x^2 + 18 \]
they are going to be +-factors of the constant, or of 18
in this case numbers
+-1, +-2, +-3, +-6, +-9
plug each one which of them work.

Answer 2

list all the factors of 18 and all of the factors of 2

Answer 3

18 factors are 1, 2, 3, 6, 9, 18
factors of 2 are 1, 2

Answer 4

So I do the plain number, and the first number? I totally forgot the correct terms for those. -_-

Answer 5

1,2,3,6,9,18 over 1 is 1,2,3,6,9,18
1,2,3,6,9, 18 over 2 is 1/2, 2/2 which is 1, 3/2, 6/2 which is 3, 9/2 and 18/2 which is 9. You do not need to list 1, 3, and 9 more than once.
Also, don't forget the plus and minus signs in front of all of them

Answer 6

You are just writing out all of the possibles. You do not need to factor your polynomial out. You are just listing the possible solutions. The theorem does not guarantee that any are the actual zeros.

Answer 7

I have to list the fractions, too? Why?

Answer 8

Oh, I see. Nevermind. Thanks, guys. God bless. C:

Answer 9

Wait, @precal , when I list all of the possibilities, do I include the numbers we used to divide, (1, 2, 3, 6, 9), or just what came from our division, (/2, 3/2)?

Answer 10

\[\pm \frac{18}{1}, \pm\frac{18}{2}, \pm\frac{9}{1}, \pm\frac{9}{2}, \pm\frac{6}{1}, \pm\frac{6}{2}, \pm\frac{3}{1}, \pm\frac{3}{2}, \pm\frac{2}{1}, \pm\frac{2}{2}, \pm\frac{1}{1}, \pm\frac{1}{2}\]

Answer 11

Cull out the duplicates.

Answer 12

Thank you! God bless! :D

Answer 13

yw

Answer 14

Yes, follow Mertsj's advice....sorry I log off too soon to help you