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ALEKS LTI 1.3
ALEKS - Brittney Smith - Pre

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Proctored Test 3 16-Wks (Lectures 1-11)
Question 11 of 18 (1 point) I Question Attempt: 1 of 1

=1

-=2

-=3
4

=5

=6

=7

-=8
Suppose that the polynomial function 
f is defined as follows.

f(x)=2x^(2)(x-4)^(2)(x+7)^(3)
List each zero of 
f according to its multiplicity in the categories below.
If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on " 
N
Zero(s) of multiplicity one: 
◻

◻
Zero(s) of multiplicity two: 
◻
Zero(s) of multiplicity three: 
◻




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Suppose that the polynomial function ff is defined as follows.\newlinef(x)=2x2(x4)2(x+7)3f(x)=2x^{2}(x-4)^{2}(x+7)^{3}\newlineList each zero of ff according to its multiplicity in the categories below.\newlineIf there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "N"\newlineZero(s) of multiplicity one: \newline\newlineZero(s) of multiplicity two: \newline\newlineZero(s) of multiplicity three: \newline\newline

Full solution

Q. Suppose that the polynomial function ff is defined as follows.\newlinef(x)=2x2(x4)2(x+7)3f(x)=2x^{2}(x-4)^{2}(x+7)^{3}\newlineList each zero of ff according to its multiplicity in the categories below.\newlineIf there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "N"\newlineZero(s) of multiplicity one: \newline\newlineZero(s) of multiplicity two: \newline\newlineZero(s) of multiplicity three: \newline\newline
  1. Identify Zeros: Identify zeros from the polynomial f(x)=2x2(x4)2(x+7)3f(x) = 2x^2(x-4)^2(x+7)^3.f(x)=0f(x) = 0 when x=0x = 0, x=4x = 4, or x=7x = -7.
  2. Determine Multiplicity: Determine the multiplicity of each zero.\newlinex=0x = 0 appears in the term x2x^2, so its multiplicity is 22.\newlinex=4x = 4 appears in the term (x4)2(x-4)^2, so its multiplicity is 22.\newlinex=7x = -7 appears in the term (x+7)3(x+7)^3, so its multiplicity is 33.
  3. Categorize Zeros: Categorize zeros by their multiplicity.\newlineZero(s) of multiplicity one: None.\newlineZero(s) of multiplicity two: 00, 44.\newlineZero(s) of multiplicity three: 7-7.

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