Final answer:
The degree of a polynomial is determined by the term with the highest power of x. The coefficients are the numbers that multiply each term. The factors of a polynomial are the values that make it equal to zero when substituted into the polynomial. The end behavior of a polynomial describes how the values of y behave as x approaches positive or negative infinity. The requested polynomial calculator typically determines options are A) Degree of the polynomial and B) Coefficients of the polynomial.
Step-by-step explanation:
In order to find the degree of a polynomial, we need to identify the term with the highest power of x.
This term will determine the degree of the polynomial.
For example, if the highest power of x is 3, then the degree of the polynomial is 3.
The coefficients of a polynomial are the numbers that multiply each term. For example, in the polynomial 2x^3 + 4x^2 - 3x + 1, the coefficients are 2, 4, -3, and 1.
The factors of a polynomial are the values that, when substituted into the polynomial, make it equal to zero.
To find the factors, we can use methods such as synthetic division or factoring by grouping.
The end behavior of a polynomial describes how the values of y behave as x approaches positive or negative infinity.
We can determine the end behavior by looking at the leading term of the polynomial and its degree.
If the leading term has a positive coefficient and even degree, the end behavior is positive infinity for both x approaches.
If the leading term has a positive coefficient and odd degree, the end behavior is positive infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.
Conversely, if the leading term has a negative coefficient and even degree, the end behavior is negative infinity for both x approaches.
If the leading term has a negative coefficient and odd degree, the end behavior is negative infinity as x approaches positive infinity and positive infinity as x approaches negative infinity.
The requested polynomial calculator typically determines options are A) Degree of the polynomial and B) Coefficients of the polynomial.