Algebra II 1st Semester Review (Topics 3 & 4) 2004

Front

What is a leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the end behavior of the polynomial function.

Front

How do you determine if a polynomial has a positive or negative leading coefficient?

Back

Look at the coefficient of the term with the highest degree. If it is greater than zero, the leading coefficient is positive; if less than zero, it is negative.

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial has an even degree if the highest exponent of its variable is an even number. This affects the graph's end behavior.

Front

What does it mean for a polynomial to have an odd degree?

Back

A polynomial has an odd degree if the highest exponent of its variable is an odd number. This affects the graph's end behavior.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n roots in the complex number system, counting multiplicities.

Front

How do you find the total number of roots of a polynomial?

Back

The total number of roots of a polynomial is equal to its degree, which is the highest exponent of the variable in the polynomial.

Front

What is a y-intercept in a polynomial function?

Back

The y-intercept is the point where the graph of the polynomial crosses the y-axis, found by evaluating the polynomial at x=0.

Front

How do you simplify a rational expression?

Back

To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

Front

What is the process for factoring a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to the constant term and add to the linear coefficient, then rewrite the expression.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a mathematical expression consisting of variables raised to whole number powers, while a rational function is a ratio of two polynomials.