write a third degree polynomial with integral coefficients if zeros are "-1," "-4," and 5

Question

write a third degree polynomial with integral coefficients if zeros are &quot;-1,&quot; &quot;-4,&quot; and 5

Vasquez · Accepted Answer

To write a third-degree polynomial with integral coefficients given the zeros -1, -4, and 5, we can use the fact that if a polynomial has a zero at a particular value, then the polynomial can be factored as (x - zero).
Using this information, we can write the polynomial as:

p (x) = (x - (- 1)) (x - (- 4)) (x - 5)

Simplifying further:

p (x) = (x + 1) (x + 4) (x - 5)

Expanding the expression:

p (x) = (x^{2} + 5 x + 4) (x - 5)

Multiplying the binomials:

p (x) = (x^{3} + 5 x^{2} + 4 x - 5 x^{2} - 25 x - 20)

p (x) = (x^{3} - 20 x - 20)

Therefore, the third-degree polynomial with integral coefficients and zeros -1, -4, and 5 is

p (x) = x^{3} - 20 x - 20

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write a third degree polynomial with integral coefficients

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