Solving Polynomial Equations

Front

What is a polynomial equation?

Back

A polynomial equation is an equation that involves a polynomial expression, which is a sum of terms, each consisting of a variable raised to a non-negative integer power and multiplied by a coefficient.

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 is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c), which uses coefficients instead of variables.

Front

What is the difference of cubes formula?

Back

The difference of cubes formula states that a³ - b³ = (a - b)(a² + ab + b²).

Front

What is the sum of cubes formula?

Back

The sum of cubes formula states that a³ + b³ = (a + b)(a² - ab + b²).

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 an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

What is a root of a polynomial?

Back

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

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 the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or root) 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.