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Find a polynomial f (x) of degree 4 that has the following zeros.

-7, 0, 2, 3
Leave your answer in factored form.

Find a polynomial f (x) of degree 4 that has the following zeros. -7, 0, 2, 3 Leave-example-1

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Explanation:

the multiplication of multiple factors is zero, if at least one factor is zero.

and to get a polynomial of degree 4 (that means there is a term of x⁴) we need 4 factors each a term in x. so, x×x×x×x = x⁴.

it is nice to get all 4 zeros defined. these zeroes mean that f(x) = 0 for x = -7, x = 0, x = 2 and x = 3.

how do we make sure that is the case ?

by defining corresponding factors for f(x).

f(x) = (x + 7)x(x - 2)(x - 3)

that function is 0 for x = -7, x = 0, x = 2, x = 3.

done.

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