Which is the polynomial function of lowest degree
that has -5.-2, and 0 as roots?
fx) = (x-2)(x-5)
F(x) = x(x-2)(x-5)
FX)=x + 2)x+5)
f(x) = x(x + 2)(x+5)

Option D:

f(x) = x(x + 2)(x + 5)

Solution:

Given root of the polynomial functions are:

–5, –2 and 0.

If a is the root of the polynomial then the factor is (x –a).

So that, the factors of the given roots are:

(x –(–5)) = x + 5

(x –(–2)) = x + 2

(x – 0) = x

Polynomial = Product of the factors

             f(x) = (x + 5)(x + 2)x

Switch the order of the factors.

             f(x) = x(x + 2)(x + 5)

Option D is the correct answer.

The polynomial function of lowest degree is f(x) = x(x + 2)(x + 5).

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