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1 : Consider the function $f(x) = \sage {p1f1} + \sage {p1f2} + \sage {p1f3} + \sage {p1f4}$. According to the Fundamental Theorem of Algebra, how many (possibly complex-valued) zeros are there for $f(x)$? $\answer {\sage {p1ans1}}$
1.1 : There are at least exactly at most $\answer {\sage {p1ans1}}$ real-valued solutions.
1.1.1 : This means there could be more than exactly less than $\sage {p1ans1}$ real-valued zeros.
1.2 : What is the leading term in this polynomial? $\answer {\sage {p1ans2}}$
1.3 : What is the leading coefficient in this polynomial? $\answer {\sage {p1ans3}}$
2 : Consider the function $f(x) = \sage {p2f1} + \sage {p2f2} + \sage {p2f3} + \sage {p2f4}$. According to the Fundamental Theorem of Algebra, how many (possibly complex-valued) zeros are there for $f(x)$? $\answer {\sage {p2ans1}}$
2.1 : There are at least exactly at most $\answer {\sage {p2ans1}}$ real-valued solutions.
2.1.1 : This means there could be more than exactly less than $\sage {p2ans1}$ real-valued zeros.
2.2 : What is the leading term in this polynomial? $\answer {\sage {p2ans2}}$
2.3 : What is the leading coefficient in this polynomial? $\answer {\sage {p2ans3}}$
3 : Consider the function $f(x) = \sage {p3f1} + \sage {p3f2} + \sage {p3f3} + \sage {p3f4}$. According to the Fundamental Theorem of Algebra, how many (possibly complex-valued) zeros are there for $f(x)$? $\answer {\sage {p3ans1}}$
3.1 : There are at least exactly at most $\answer {\sage {p3ans1}}$ real-valued solutions.
3.1.1 : This means there could be more than exactly less than $\sage {p3ans1}$ real-valued zeros.
3.2 : What is the leading term in this polynomial? $\answer {\sage {p3ans2}}$
3.3 : What is the leading coefficient in this polynomial? $\answer {\sage {p3ans3}}$