5.1-5.4

Front

What are the roots of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero.

Front

How do you determine the number of zeros needed for synthetic division?

Back

The number of zeros needed corresponds to the degree of the polynomial minus the number of known roots.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

Front

What is the zero-product property?

Back

If the product of two or more factors is zero, at least one of the factors must be zero.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for x.

Front

What is the result of multiplying (a + b)(c + d)?

Back

The result is ac + ad + bc + bd, which is known as the distributive property.

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 does it mean for a polynomial to be factored completely?

Back

A polynomial is factored completely when it is expressed as a product of irreducible polynomials.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

How do you check if a division problem is worked correctly?

Back

You can check by multiplying the quotient by the divisor and comparing it to the original dividend.