Use the Rational Roots Test to Find All Possible Roots f(x)=x^4-5x^3-36x^2+272x-448

$f (x) = x^{4} - 5 x^{3} - 36 x^{2} + 272 x - 448$

Step 1

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 2, \pm 4, \pm 7, \pm 8, \pm 14, \pm 16, \pm 28, \pm 32, \pm 56, \pm 64, \pm 112, \pm 224, \pm 448$

$q = \pm 1$

Step 2

Find every combination of $\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

$\pm 1, \pm 2, \pm 4, \pm 7, \pm 8, \pm 14, \pm 16, \pm 28, \pm 32, \pm 56, \pm 64, \pm 112, \pm 224, \pm 448$

Use the Rational Roots Test to Find All Possible Roots f(x)=x^4-5x^3-36x^2+272x-448

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