PCX Chapter 2 FE Review

Front

What are the possible rational roots of a polynomial?

Back

The possible rational roots of a polynomial can be found using the Rational Root Theorem, which states that any rational solution, expressed as a fraction p/q, has p as a factor of the constant term and q as a factor of the leading coefficient.

Front

What is the significance of roots in a polynomial function?

Back

Roots (or zeros) of a polynomial function are the values of x for which the function equals zero. They indicate where the graph of the function intersects the x-axis.

Front

What does multiplicity of a root mean?

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. A root with an even multiplicity will touch the x-axis, while a root with an odd multiplicity will cross the x-axis.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the leading term. If the leading coefficient is positive and the degree is even, the ends of the graph will rise. If the leading coefficient is negative and the degree is odd, the left end will rise and the right end will fall.

Front

What is a polynomial function of degree 3?

Back

A polynomial function of degree 3, also known as a cubic function, can be expressed in the form P(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for x. This can involve factoring, using the quadratic formula, or synthetic division.

Front

What is the relationship between the degree of a polynomial and the number of roots?

Back

The degree of a polynomial function indicates the maximum number of roots it can have. For example, a polynomial of degree 3 can have up to 3 roots.

Front

What is the role of the leading coefficient in a polynomial?

Back

The leading coefficient of a polynomial determines the direction of the graph's end behavior and affects the steepness of the graph.

Front

How do you identify the roots of a polynomial from its graph?

Back

The roots of a polynomial can be identified from its graph as the x-coordinates where the graph intersects the x-axis.

Front

What is the process of synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear factor. It involves using the coefficients of the polynomial and the root of the divisor.