\(P(x) = x^6 – 2x^2 – 3x^7 + 7 = -3x^7 + x^6 – 2x^2 + 7\)

1) The degree of the polynomial. = 7

2) The leading term of the polynomial. \(= -3x^7\)

3) The leading coefficient of the polynomial. = -3

asked 2021-05-09

For each polynomial, state the constant term, the leading coefficient, and the degree of the polynomial.

\(5x^{2}-6x^{3}+3x^{6}+7\)

\(5x^{2}-6x^{3}+3x^{6}+7\)

asked 2021-06-14

For the following exercise, for each polynomial, 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; and e. determine algebraically whether the polynomial is even, odd, or neither.

\(\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{2}}-{3}{x}-{5}\)

\(\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{2}}-{3}{x}-{5}\)

asked 2021-05-05

For each polynomial, state the constant term, the leading coefficient, and the degree of the polynomial.

\(5x^{2}-8x+2x^{4}-3\)

\(5x^{2}-8x+2x^{4}-3\)

asked 2021-06-07

For the following exercise, for each polynomial, 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; and e. determine algebraically whether the polynomial is even, odd, or neither.

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}+{3}{x}^{{2}}-{x}-{3}\)

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}+{3}{x}^{{2}}-{x}-{3}\)

asked 2021-05-04

For the following exercise, for each polynomial, 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; and e. determine algebraically whether the polynomial is even, odd, or neither.

\(\displaystyle{f{{\left({x}\right)}}}=-{3}{x}^{{2}}+{6}{x}\)

\(\displaystyle{f{{\left({x}\right)}}}=-{3}{x}^{{2}}+{6}{x}\)

asked 2021-05-11

Consider the polynomial function \(p(x)=(3x^{2}-5x-2)(x-5)(x^{2}-4)\).

A) what is the degree of the polynomial? What is the y intercept of the function?

B)What are the zeros and their multiplicities?

C) what is the leading term of the polynomial and what power function has a graph most similiar to the graph of p?

A) what is the degree of the polynomial? What is the y intercept of the function?

B)What are the zeros and their multiplicities?

C) what is the leading term of the polynomial and what power function has a graph most similiar to the graph of p?

asked 2021-02-02

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

asked 2021-01-05

asked 2021-05-17

For the following exercise, for each polynomial, 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; and e. determine algebraically whether the polynomial is even, odd, or neither. \(\displaystyle{f{{\left({x}\right)}}}={3}{x}−{x}^{{3}}\)

asked 2021-07-01

Find a degree 3 polynomial having zeros -6, 6 and 0 and leading coefficient equal to 1