Step 1. The expression that we have is:
[tex]a^2-6a^3+8-a[/tex]
To write the polynomial in descending order we need to put first the term with the major exponent, and then place the following terms in descending order according to their exponent. The result is:
[tex]\begin{gathered} Descending\text{ order:} \\ -6a^3+a^2-a+8 \end{gathered}[/tex]
Step 2. The leading term is the term (including coefficient and variable) that is at the beginning of the expression when we place the polynomial in descending order, the one that has the greatest degree:
[tex]\begin{gathered} Leading\text{ term: } \\ -6a^3 \end{gathered}[/tex]
Step 3. The leading coefficient is only the number that accompanies the variable in the leading term:
[tex]\begin{gathered} Leading\text{ coefficient: } \\ -6 \end{gathered}[/tex]
Step 4. The number of terms in the number of individual expressions separated by '+' or '-' we have in our polynomial:
[tex]\begin{gathered} Number\text{ of terms: } \\ 4 \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} Descending\text{ order:}-6a^3+a^2-a+8 \\ Leading\text{ term:}-6a^3 \\ Leading\text{ coefficient:}-6 \\ Number\text{ of terms: }4 \end{gathered}[/tex]
