Problem

Find the degree, leading term, and leading coefficient of the polynomial function P(x)=4x5−3x4+2x3−x2+5x−6.

Answer

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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.

Steps

Step 1 ：The degree of a polynomial function is the highest power of the variable in the polynomial. In the given polynomial P(x)=4x5−3x4+2x3−x2+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 4x5.

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.

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