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What is a cubic polynomial function in standard form with zeros 5, 2, and -5?

1 Answer

Mar 30, 2016

$f (x) = x^{3} - 2 x^{2} - 25 x + 50$ $f(x) = x^3-2x^2-25x+50$

Explanation:

$f (x) = (x - 5) (x + 5) (x - 2)$ $f(x) = (x-5)(x+5)(x-2)$

$= (x^{2} - 25) (x - 2)$ $= (x^2-25)(x-2)$

$= x^{3} - 2 x^{2} - 25 x + 50$ $= x^3-2x^2-25x+50$

Standard form sorts the powers of $x$ $x$ (or whatever variable you are using) in descending order.

Any polynomial in $x$ $x$ with these zeros will be a multiple (scalar or polynomial) of this $f (x)$ $f(x)$ .

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