Practice 4.7

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).

Tags

CCSS.HSA.APR.B.2

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 x. This can involve factoring, using the quadratic formula, or synthetic division.

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 primarily for polynomials.

Tags

CCSS.HSA.APR.D.6

Front

What are rational zeros?

Back

Rational zeros are potential solutions to a polynomial equation that can be expressed as a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Tags

CCSS.HSA.APR.B.2

Front

What is the Factor Theorem?

Back

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

Tags

CCSS.HSA.APR.B.2

Front

How do you determine if (x - c) is a factor of a polynomial?

Back

To determine if (x - c) is a factor of a polynomial, evaluate the polynomial at c. If the result is zero, then (x - c) is a factor.

Tags

CCSS.HSA.APR.B.2

Front

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

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It affects the end behavior of the polynomial's graph.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. It determines the polynomial's behavior and the number of possible zeros.

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 real zeros, counting multiplicities.

Front

What is the process of factoring a polynomial?

Back

Factoring a polynomial involves rewriting it as a product of its factors, which can include linear factors and irreducible polynomials.