HW23 - Polynomial practice

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What are the coefficients in a polynomial?

Back

Coefficients are the numerical factors in a polynomial that multiply the variable terms.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - 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.

Front

What is the Remainder Theorem?

Back

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

What is the significance of the leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree and determines the end behavior of the polynomial graph.

Front

How do you perform synthetic division?

Back

To perform synthetic division, write the coefficients of the polynomial, use the root of the divisor, and follow the synthetic division algorithm.

Front

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

Back

A polynomial of degree n can have at most n zeros, counting multiplicities.