Question

Use the Rational Zero Theorem to list all possible rational zeros for the given function.
f(x) = -2x3 + 4x2 - 2x + 8

Answer 1

@kl0723

Answer 2

factors of the constant or

all factors of the constant
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all factors of the leading coefficient

Answer 3

list the factors of -2

list the factors of 8

use the advice above

Answer 4

Factors of 8: 1, 2, 4, 8
Factors of 2: 1, 2
Possible rational zeros are: \(\Large \pm \frac{1, 2, 4, 8}{1, 2} = ?\)

Answer 5

it's not meant to taken literally. It's short for saying each factor of the constant over each factor of the leading coneffient

Answer 6

\(\Large \pm \frac{1, 2, 4, 8}{1, 2} = \)
\(\Large \pm \frac 11, \pm \frac 12, \pm \frac 21, \pm \frac 22, ...\) (complete the list)

Remove duplicate items and list them in increasing order.

Answer 7

why is it that -1, 2 ,-2, 4, -4 are not working as factors?

Answer 8

I give

Answer 9

are all the signs in the original correct?

Answer 10

f(x) = -2x^3 + 4x^2 - 2x + 8

Answer 11

it's ok thanks for checking.
possible rational---------------
the solution was not rational on the calculator it had 1 value for x at 2.315

Answer 12

The rational roots theorem just gives possible factors. Sometimes none of them are factors as is the case here. But for this problem, they don't ask to find the roots or factor. They just want a list of possible rational factors.

Answer 13

yes thanks