Question

1112 Question 12 3 4 56 789 10 1/1 13/14 2/2 1/1 2/2 44 0/1 2/2 2/2 0/1 1/1 2/2 Points Assignment Submission For this assignment, you submit answers by questions. You are required to use a new Assignment Scoring Your best submission for each entire question is used for your score. : 24. О 011 points l Previous Answers SPreCalc7 3.3.063.MI. 1/3 Submissions Used Find a polynomial of the specified degree that has the given zeros. Degree 3; zeros -2, 2, 4 P(x) Need Help?Read It Watch It Master It Show My Work (optonan) Submit Answer Save Progress

Answer 1

We want A polynomial of degree 3 having $-2,2,4$ as roots

The polynomial must be of the form $p(x)=c(x-(-2))(x-2)(x-4)$ for some $0\neq c\in\mathbb{R}$

Thus, the polynomial must be of the form $p(x)=c(x+2)(x-2)(x-4)=c(x^2-4)(x-4)$

Expanding this, we get $p(x)=c(x^3-4x^2-4x+16)$

Taking $c=1$, one possible answer is $p(x)={\color{Red} x^3-4x^2-4x+16}$

$\blacksquare$

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