Indicate whether the expression defines a polynomial function. P(x) = −x2 + 3x + 3 polynomial or not a polynomial If it is a polynomial function, identify the following. (If it is not a polynomial function, enter DNE for all three answers.) (a) Identify the leading coefficient. (b) Identify the constant term. (c) State the degree.

Question
Polynomial arithmetic
asked 2021-02-20
Indicate whether the expression defines a polynomial function. \(\displaystyle{P}{\left({x}\right)}=−{x}{2}+{3}{x}+{3}\) polynomial or not a polynomial If it is a polynomial function, identify the following. (If it is not a polynomial function, enter DNE for all three answers.) (a) Identify the leading coefficient. (b) Identify the constant term. (c) State the degree.

Answers (1)

2021-02-21
Definition used: “A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non- negative integer exponents of variables. The polynomial equation is of the form \(\displaystyle{c}_{{n}}{x}^{{{n}}}+{c}_{{{n}-{1}}}{x}^{{{n}-{1}}}+\ldots+{c}_{{2}}{x}^{{2}}+{c}_{{1}}{x}+{c}_{{0}}\) Here, c, is the leading coefficient, n is the highest degree and the constant is a) The given function is \(\displaystyle{P}{\left({x}\right)}=−{x}{2}+{3}{x}+{3}.\) By the definition of polynomial, the above function is quadratic polynomial. The leading coefficient is –1. b) By the definition of polynomial equation, the constant term is 3. c) By the definition of polynomial equation, the degree is 2.
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