Ch 4 Test Review

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial is expressed as a product of its factors, which can be linear or quadratic expressions.

Front

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

Back

The end behavior of a polynomial function is determined by the leading term's degree and its leading coefficient. If the degree is even and the leading coefficient is positive, both ends go to positive infinity. If the degree is even and the leading coefficient is negative, both ends go to negative infinity. If the degree is odd and the leading coefficient is positive, the left end goes to negative infinity and the right end goes to positive infinity. If the degree is odd and the leading coefficient is negative, the left end goes to positive infinity and the right end goes to negative infinity.

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of lower degree, similar to numerical long division.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression of the form ax^2 + bx + c, look for two numbers that multiply to ac and add to b. Then, rewrite the expression using these numbers to factor it.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is expressed as a sum of terms in descending order of degree, such as a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0.

Front

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

Back

A polynomial is a mathematical expression consisting of variables raised to non-negative integer powers, while a rational function is a ratio of two polynomials.

Front

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

Back

The leading coefficient of a polynomial determines the direction of the graph as x approaches positive or negative infinity and influences the end behavior.

Front

What are the steps to factor a trinomial?

Back

To factor a trinomial of the form ax^2 + bx + c, identify two numbers that multiply to ac and add to b, rewrite the middle term using these numbers, and then factor by grouping.