Factor and Solve Polynomials

Front

Define 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 expression.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.

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 synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.

Front

If x = 7 is a zero of a polynomial, what number do you use for synthetic division?

Back

You use -7 for synthetic division.

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or zero) of a polynomial equation 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.

Front

How do you factor by grouping?

Back

To factor by grouping, group terms with common factors, factor out the common factors, and then factor out the common binomial.

Front

What is the significance of the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial has at least one complex root.