P(x) = x^6 – 2x^2 – 3x^7 + 7 = -3x^7 + x^6 – 2x^2 + 7
1) The degree of the polynomial.
= 7
2) The leading term of the polynomial.
= -3x^7
3) The leading coefficient of the polynomial.
= -3

Question

asked 2020-12-22

For the following polynomial, P(x) =x^3 – 2x^2 + 4x^5 + 7, what is:
1) The degree of the polynomial,
2) The leading term of the polynomial,
3) The leading coefficient of the polynomial.

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.

asked 2020-12-30

Indicate whether the expression defines a polynomial function.
\(\displaystyle{g{{\left({x}\right)}}}=−{4}{x}^{{5}}−{3}{x}^{{2}}+{x}−{2}\)
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.

asked 2021-01-05

Determine whether the following are polynomials or not:
2x^2 + 7x+ 1,
1/(x^3 + 2),
6,
8x – 1,
sqrt(2x + 5).

asked 2021-01-19

Factor the trinomial. Note that the coefficient of \(\displaystyle{x}^{{2}}\) is not equal to 1.
\(\displaystyle{4}{x}^{{2}}–{3}{x}={10}.\)

asked 2021-01-04

The polynomial \(\displaystyle{y}=-{0.79}{x}^{{4}}+{3}{x}^{{3}}+{27.3}\) describes the billions of flu virus particles in a person’s body x days after being infected. Find the number of virus particles, in billions, after 1 day.

asked 2021-02-02

Find a second-degree polynomial P such that P(4)=5, P'(4)=3, and P"(4)=3

asked 2021-02-25

Find a polynomial of the specified degree that has the given zeros. Degree 4, zeros -2, 0, 2, 4

asked 2020-11-01

For the following exercise, for each polynomial \(\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{2}}}}{x}^{{{2}}}\ -\ {1}\):
a) find the degree,
b) find the zeros, if any,
c) find the y-intercept(s), if any,
d) use the leading coefficient to determine the graph’s end behavior,
e) determine algebraically whether the polynomial is even, odd, or neither.

asked 2021-02-03

Tell whether 5x^(1/2) – 3x^3 is a polynomial.