Find the degree, leading term, and leading coefficient of the polynomial function \( P(x) = 4x^{5} - 3x^{4} + 2x^{3} - x^{2} + 5x - 6 \).
Answer
The leading coefficient of a polynomial function is the coefficient of the term with the highest power of the variable. Therefore, in the given polynomial, the leading coefficient is 4.
Step 1 ：The degree of a polynomial function is the highest power of the variable in the polynomial. In the given polynomial \( P(x) = 4x^{5} - 3x^{4} + 2x^{3} - x^{2} + 5x - 6 \), the highest power of x is 5. Therefore, the degree of the polynomial is 5.
Step 2 ：The leading term of a polynomial function is the term with the highest power of the variable. Therefore, in the given polynomial, the leading term is \( 4x^{5} \).
Step 3 ：The leading coefficient of a polynomial function is the coefficient of the term with the highest power of the variable. Therefore, in the given polynomial, the leading coefficient is 4.
