Find a polynomial of the specified degree that has the given zeros. Degree 4, zeros -2, 0, 2, 4

Nann 2021-02-25 Answered
Find a polynomial of the specified degree that has the given zeros. Degree 4, zeros -2, 0, 2, 4
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comentezq
Answered 2021-02-26 Author has 106 answers
Recall, according to the factor theorem the expression (xc) is a factor of a polynomial P(x) if and only if P(c) = 0.
1) Let a polynomial function P(x):
If c = -2 is a zero of P(x) the expression (x+2) is a factor of P(x).
If c = 0 is a zero of P(x) the expression (x0)= is a factor of P(x).
If c = 2 is a zero of P(x) the expression (x2)= is a factor of P(x).
If c = 4 is a zero of P(x) the expression (x4)= is a factor of P(x).
2) The polynomial P(x) can be written in factored form as:
P(x) =x(x4)(x+2)(x2)
P(x) =(x24x)(x+2)(x2)
3) Apply the difference of squares identity: a2b2=(a+b)(ab)
P(x) =(x24x)(x24)
P(x) =x44x34x2+16x
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