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Math  /  Algebra

QuestionHolden Warren Question 7 of 13 PREV NEXT
The polynomial function p(x)=x3+7x2+20x+24p(x)=x^{3}+7 x^{2}+20 x+24 has x=−3x=-3 as a root. What are the remaining roots of p(x)p(x) ? Separate multiple answers with a comma. \qquad \begin{tabular}{lr} \hline Question 1 & 100%100 \% \\ \hline Question 2 & 100%100 \% \\ \hline Question 3 & 100%100 \% \\ Question 4 & 50%50 \% \\ Question 5 & 50%50 \% \\ Question 6 & 100%100 \% \\ \hline \end{tabular}
Enter the factored form of p(x)p(x). Question 7 Question 8 Question 9 Question 10 Question 11

Studdy Solution
The remaining roots of p(x)p(x) are −2+2i-2 + 2i and −2−2i-2 - 2i.
The factored form of p(x)p(x) is p(x)=(x+3)(x−(−2+2i))(x−(−2−2i))p(x) = (x+3)(x - (-2 + 2i))(x - (-2 - 2i)), which simplifies to p(x)=(x+3)(x+2−2i)(x+2+2i)p(x) = (x+3)(x+2-2i)(x+2+2i).

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