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How do you write a polynomial function of least degree with integral coefficients that has the given zeros 3, 2, -2?

1 Answer

Mar 22, 2016

$f (x) = (x - 3) (x - 2) (x + 2) = x^{3} - 3 x^{2} - 4 x + 12$ $f(x) = (x-3)(x-2)(x+2)=x^3-3x^2-4x+12$

Explanation:

$f (x) = (x - 3) (x - 2) (x + 2)$ $f(x) = (x-3)(x-2)(x+2)$

$= (x - 3) (x^{2} - 4)$ $=(x-3)(x^2-4)$

$= x^{3} - 3 x^{2} - 4 x + 12$ $=x^3-3x^2-4x+12$

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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