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How do you write a polynomial function given the real zeroes -5,2,-2 and coefficient 1?

1 Answer

Nov 13, 2015

$f (x) = x^{3} + 5 x^{2} - 4 x - 20$ $f(x)=x^3+5x^2-4x-20$

Explanation:

$(x + 5) (x - 2) (x + 2) = 0$ $(x+5)(x-2)(x+2) = 0$ if $x \in {- 5, 2, - 2}$ $x in {-5, 2, -2}$
$XXX$ $color(white)("XXX")$ Since for any value of $x$ $x$ in this set
$XXX$ $color(white)("XXX")$ one of the terms will be $= 0$ $=0$

$(x + 5) (x - 2) (x + 2)$ $(x+5)(x-2)(x+2)$
$XXX = (x + 5) (x^{2} - 4)$ $color(white)("XXX")=(x+5)(x^2-4)$
$XXX = x^{2} + 5 x^{2} - 4 x - 20$ $color(white)("XXX")=x^2+5x^2-4x-20$

(I assume when the questions says "coefficient 1" it means the coefficient of the highest order term).

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