Question

Indicate whether the expression defines a polynomial function. P(x) = -x^{2}+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.)

Polynomial arithmetic
ANSWERED
asked 2021-08-08
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)

2021-08-09
Step 1
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
\(\displaystyle{c}_{{{n}}}{x}^{{{n}}}+{c}_{{{c}-{1}}}{x}^{{{n}-{1}}}+\cdots+{c}_{{{2}}}{x}^{{{2}}}+{c}_{{{1}}}{x}+{c}_{{{0}}}\)
Here, \(\displaystyle{c}_{{{n}}}\) is the leading coefficient, n is the highest degree and the constant is \(\displaystyle{c}_{{{0}}}\)."
Step 2
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.
Step 3
b)
By the definition of polynomial equation, the constant term is 3.
Step 4
c)
By the definition of polynomial equation, the degree is 2.
0
 
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