Question

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

f(x) = -2x4 + 4x3 + 3x2 + 18
Show work to receive credit.

Answer 1

1. find all factors of leading coefficient
2. find all factors of constant term

Answer 2

how would I find the factors of leading coefficient and constant term?

Answer 3

wats the leading coefficent here ?

Answer 4

-2?

Answer 5

is it?

Answer 6

yes. so factors are just \(\pm 1, \pm 2\)

Answer 7

similarly find factors for constant term also

Answer 8

ok so 1 and 2 are possible rational zeros of the function?

Answer 9

nope we're not finished yet.

Answer 10

Find factors of constant term, them we can figure out the possible rational roots

Answer 11

*then

Answer 12

are the factors of the constant term 1,2, and 4?

Answer 13

you missed a few

Answer 14

and 4 is not a factor of 18. 4 doesnt divide 19

Answer 15

factors of a number are just all the numbers that divide it.

Answer 16

for ex, 9 is a factor of 18, cuz 9 divides 18

Answer 17

so its 1 2 and 3 then in this case

Answer 18

thats all ?

Answer 19

factors of 18 : \(\pm 1 , \pm 2, \pm 3, \pm 6, \pm 9, \pm 18\)

Answer 20

so since we have all the factors for the function, do we start finding the possible rational zeros for the function?

Answer 21

yes, possible rational zeroes are just the fraction of factors of 'constant term' and 'leading coeffecient'

Answer 22

oh ok. can you draw it out so I can see the work better? if you can, that'd be nice

Answer 23

factors of constant term : \(\pm 1 , \pm 2, \pm 3, \pm 6, \pm 9, \pm 18 \)
factors of leading coeff : \(\pm 1 , \pm 2\)

possible rational zeroes :

\(\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{3}{1},\pm\frac{6}{1},\pm\frac{9}{1},\pm\frac{18}{1} \)

and,

\(\pm\frac{1}{2},\pm\frac{2}{2},\pm\frac{3}{2},\pm\frac{6}{2},\pm\frac{9}{2},\pm\frac{18}{2} \)

Answer 24

simplify the fractions

Answer 25

so the simplified fractions would be: 1, 2, 3, 6, 9, and 18
as well as 1/2, 1, 3/2, 3, 9/2, and 9. is this right?

Answer 26

thats right, arrange them in order

Answer 27

possible rational zeroes : \(\pm 1/2, \pm 1, \pm 3/2, \pm 3, \pm 9/2, \pm 6, \pm 9, \pm 18\)

Answer 28

dont forget the negative ones !

Answer 29

oh ok and thank you so much! and I won't

Answer 30

np :)