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 $\left(x\u2013c\right)$ 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$\left(x\u20130\right)=$ is a factor of P(x).

If c = 2 is a zero of P(x) the expression$\left(x\u20132\right)=$ is a factor of P(x).

If c = 4 is a zero of P(x) the expression$\left(x\u20134\right)=$ is a factor of P(x).

2) The polynomial P(x) can be written in factored form as:

P(x)$=x\left(x\u20134\right)(x+2)\left(x\u20132\right)$

P(x)$=\left({x}^{2}\u20134x\right)(x+2)\left(x\u20132\right)$

3) Apply the difference of squares identity:${a}^{2}\u2013{b}^{2}=(a+b)\left(a\u2013b\right)$

P(x)$=\left({x}^{2}\u20134x\right)\left({x}^{2}\u20134\right)$

P(x)$={x}^{4}\u20134{x}^{3}\u20134{x}^{2}+16x$

1) Let a polynomial function P(x):

If c = -2 is a zero of P(x) the expression

If c = 0 is a zero of P(x) the expression

If c = 2 is a zero of P(x) the expression

If c = 4 is a zero of P(x) the expression

2) The polynomial P(x) can be written in factored form as:

P(x)

P(x)

3) Apply the difference of squares identity:

P(x)

P(x)

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