Find a polynomial of the specified degree that has the given zeros. Degree 4; ze

Lorenzolaji

Lorenzolaji

Answered question

2021-11-10

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

Answer & Explanation

Troy Lesure

Troy Lesure

Beginner2021-11-11Added 26 answers

Work as shown below, follow the steps:
Recall according to the theorem the expression
(xc)
is a factor of a polynomial
P(x)
if and only if
P(c)=0
Let a polynomial function P(x)
If c=-2 is a zero of P(x) the expression (x0)=x
is a factor of P(x) the expression (x2) is a factor of P(x)
The polynomial P(x)
can be writtenin factored form as:
P(x)=x(x4)(x+2)(x2)
P(x)=(x24x)(x+2)(x2)
[apply the difference of square identity: a2b2=(a+b)(ab)
P(x)=(x24x)(x24)
distributive property
P(x)=x44x24x3+16x
P(x)=x44x34x2+16x
Result: P(x)=x44x34x2+16x

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