a. Suppose $f(x)=-6 x^{7}+3 x^{2}+18$
i. What is the leading term of $f$ ?
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ii. What is the degree of $f$ ?
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iii. What is the leading coefficient of $f$ ?
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Answer
Final Answer: i. The leading term of $f$ is \(\boxed{-6x^7}\). ii. The degree of $f$ is \(\boxed{7}\). iii. The leading coefficient of $f$ is \(\boxed{-6}\).
Step 1 ：The leading term of a polynomial is the term with the highest degree.
Step 2 ：In the given function $f(x)=-6 x^{7}+3 x^{2}+18$, the leading term is $-6x^7$.
Step 3 ：The degree of a polynomial is the highest power of the variable in the polynomial.
Step 4 ：In the given function $f(x)=-6 x^{7}+3 x^{2}+18$, the degree is 7.
Step 5 ：The leading coefficient of a polynomial is the coefficient of the leading term.
Step 6 ：In the given function $f(x)=-6 x^{7}+3 x^{2}+18$, the leading coefficient is -6.
Step 7 ：Final Answer: i. The leading term of $f$ is \(\boxed{-6x^7}\). ii. The degree of $f$ is \(\boxed{7}\). iii. The leading coefficient of $f$ is \(\boxed{-6}\).
