How do you write a polynomial with zeros 1,-4, 5?

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How do you write a polynomial with zeros 1,-4, 5?

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Answer 1 · 2016-02-22T05:34:53

Polynomial is $(x - 1) (x + 4) (x - 5)$ $(x-1)(x+4)(x-5)$
or $x^{3} - 2 x^{2} - 19 x + 20$ $x^3-2x^2-19x+20$

Explanation:

A polynomial (say with $x$ $x$ as variable) with zeros 1,-4, 5, means that when $x$ $x$ is put equal to either $1$ $1$ , $- 4$ $-4$ or $5$ $5$ , its value reduces to zero.

Hence the polynomial would be $(x - 1) (x + 4) (x - 5)$ $(x-1)(x+4)(x-5)$

or $(x - 1) (x^{2} + 4 x - 5 x - 20)$ $(x-1)(x^2+4x-5x-20)$ (multiplying last two factors)

or $(x - 1) (x^{2} - x - 20)$ $(x-1)(x^2-x-20)$

or $x^{3} - x^{2} - 20 x - x^{2} + x + 20$ $x^3-x^2-20x-x^2+x+20$ or

$x^{3} - 2 x^{2} - 19 x + 20$ $x^3-2x^2-19x+20$

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How do you write a polynomial with zeros 1,-4, 5?

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