How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are -5, 2, -2?

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How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are -5, 2, -2?

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Answer 1 · 2017-02-28T08:53:05

$x^{3} + 5 x^{2} - 4 x - 20 = 0$ $x^3+5x^2-4x-20=0$

Explanation:

$if the zeros are - 5, 2, - 2, we write down the corresponding factors and multiply them$ $" if the zeros are" -5,2,-2, " we write down the corresponding factors and multiply them"$

zeros

$x = - 5 \Rightarrow (x + 5) = 0$ $x=-5=>(x+5)=0$

$x = 2 \Rightarrow (x - 2) = 0$ $x=2=>(x-2)=0$

$x = - 2 \Rightarrow (x + 2) = 0$ $x=-2=>(x+2)=0$

the polynomial is:

$(x + 5) (x - 2) (x + 2) = 0$ $(x+5)(x-2)(x+2)=0$

multiplying out.

$(x + 5) (x^{2} - 4) = 0 (difference of squares)$ $(x+5)(x^2-4)=0" (difference of squares)"$

$x^{3} - 4 x + 5 x^{2} - 20 = 0$ $x^3-4x+5x^2-20=0$

tidying up

$x^{3} + 5 x^{2} - 4 x - 20 = 0$ $x^3+5x^2-4x-20=0$

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How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are -5, 2, -2?

1 Answer

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