(a) $-2x^5$: degree = 5 $\\7$: degree = 0 $\\-3x^2$: degree = 2 $\\x$: degree = 1 (b) leading term = $-2x^5$ leading coefficient = $-2$ (c) degree of the polynomial = $5$
Work Step by Step
RECALL: The terms of a polynomial are separated by either an addition or a subtraction operation. Thus, the given polynomial has four terms, namely: $-2x^5$, $7$, $-3x^2$, and $x$ (a) The degree of a term is equal to the sum of the exponents of its variables. The degree of each term is: $-2x^5$: degree = 5 $\\7$: degree = 0 $\\-3x^2$: degree = 2 $\\x$: degree = 1 (b) The leading term of a polynomial is the term with the highest degree. The term with the highest degree is $-2x^5$. Thus, the leading term of the polynomial is $-2x^5$. The leading coefficient is $-2$. (c) The degree of a polynomial is equal to the degree of the leading term. Thus, the degree of the polynomial is $5$.