To determine the leading coefficient of the polynomial
[tex]\[
f(x) = 3x^2 - 0.2x^5 + 7x^3
\][/tex]
we need to follow these steps:
1. Identify the term with the highest power: The leading coefficient is associated with the term that has the highest exponent of [tex]\(x\)[/tex] in the polynomial.
2. Inspect each term:
- The first term is [tex]\(3x^2\)[/tex], where the exponent of [tex]\(x\)[/tex] is 2.
- The second term is [tex]\(-0.2x^5\)[/tex], where the exponent of [tex]\(x\)[/tex] is 5.
- The third term is [tex]\(7x^3\)[/tex], where the exponent of [tex]\(x\)[/tex] is 3.
3. Determine the highest exponent: Among the exponents 2, 5, and 3, the highest exponent is 5.
4. Identify the leading term: The term with the highest exponent is [tex]\(-0.2x^5\)[/tex].
5. Extract the leading coefficient: The coefficient of the leading term [tex]\(-0.2x^5\)[/tex] is [tex]\(-0.2\)[/tex].
Hence, the leading coefficient of the polynomial
[tex]\[
f(x) = 3x^2 - 0.2x^5 + 7x^3
\][/tex]
is
[tex]\[
\boxed{-0.2}
\][/tex]
