What are all the possible rational zeros for $f (x) = 5 x^{3} - 2 x^{2} + 20 x - 8$ $f(x)=5x^3-2x^2+20x-8$ ?

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What are all the possible rational zeros for $f (x) = 5 x^{3} - 2 x^{2} + 20 x - 8$ $f(x)=5x^3-2x^2+20x-8$ ?

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Answer 1 · 2016-10-02T00:57:35

The possible rational zeros are: $\pm 1, \pm 2, \pm 4, \pm 8, \pm \frac{1}{5}, \pm \frac{2}{5}, \pm \frac{4}{5}, \pm \frac{8}{5}$ $+-1, +-2,+-4,+-8,+-1/5,+-2/5, +-4/5, +-8/5$

Explanation:

Find the possible rational zeros of:

$f (x) = 5 x^{3} - 2 x^{2} + 2 - x - 8$ $f(x)=color(red)5x^3-2x^2+2-x-color(blue)8$

The possible rational zeros are found by dividing the factors of the constant term $8$ $color(blue)8$ (called $p$ $color(blue)p$ ) by the factors of the leading coefficient $5$ $color(red)5$ (called $q$ $color(red)q$ ).

$\frac{p}{q} = \frac{\pm 1, 2, 4, 8}{\pm 1, 5}$ $color(blue)p/color(red)q=frac{+-1,2,4,8}{+-1,5}$

Dividing each number in the numerator by each number in the denominator gives:

$\pm 1, \pm 2, \pm 4, \pm 8, \pm \frac{1}{5}, \pm \frac{2}{5}, \pm \frac{4}{5}, \pm \frac{8}{5}$ $+-1, +-2,+-4,+-8,+-1/5,+-2/5, +-4/5, +-8/5$

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What are all the possible rational zeros for $f (x) = 5 x^{3} - 2 x^{2} + 20 x - 8$ $f(x)=5x^3-2x^2+20x-8$ ?

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What are all the possible rational zeros for f(x)=5x^3-2x^2+20x-8f(x)=5x3−2x2+20x−8f(x)=5x^3-2x^2+20x-8?

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Explanation:

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What are all the possible rational zeros for $f (x) = 5 x^{3} - 2 x^{2} + 20 x - 8$ $f(x)=5x^3-2x^2+20x-8$ ?