Answered

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Write the factored form of the third-degree polynomial
function that has a positive leading coefficient and a
zero at x= -3 with a multiplicity of 3.

Sagot :

Answer:

[tex]a(x+3)^3, a \neq 0[/tex]

Step-by-step explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

Zero at x= -3 with a multiplicity of 3.

This means that:

[tex]x_1 = x_2 = x_3 = -3[/tex]

So

[tex]a(x - (-3))*(x - (-3))*(x-(-3)) = a(x+3)(x+3)(x+3) = a(x+3)^3[/tex]

Positive leading coefficient

[tex]a(x+3)^3, a \neq 0[/tex]

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