Module 5 Review Flashcardizz

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial p(x) by (x - c) is equal to p(c).

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable. The solutions are the x-values where the polynomial intersects the x-axis.

Front

What does it mean for a zero to have multiplicity?

Back

Multiplicity refers to the number of times a particular zero appears as a root of the polynomial. A zero with multiplicity greater than 1 indicates that the graph touches the x-axis at that point.

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0.

Front

What is the leading coefficient of 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's graph.

Front

How do you factor a polynomial?

Back

To factor a polynomial, look for common factors, use grouping, or apply special factoring techniques such as difference of squares or perfect square trinomials.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial. It determines the number of zeros and the general shape of the graph.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c). It is faster than long division and is used to find remainders.

Front

What is the relationship between the zeros and the factors of a polynomial?

Back

The zeros of a polynomial correspond to the values of x that make the polynomial equal to zero, and each zero can be expressed as a factor of the polynomial in the form (x - zero).

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, the graph rises to the right; if negative, it falls to the right.