Polynomials and their Operations

These flashcards cover key concepts related to polynomials, their properties, and operations such as addition, subtraction, multiplication, and factoring.

What is a polynomial made of?

A polynomial is made of terms, each consisting of a variable raised to a power and a coefficient.

How do we order the terms in a polynomial?

The terms are ordered from the term with the highest exponent to the term with the lowest exponent.

What is the degree of a polynomial?

The degree of a polynomial is the highest exponent present in any of its terms.

What are linear polynomials?

Polynomials of degree one, which graph as straight lines.

What shape does a polynomial of degree two graph as?

A parabola.

How do you add polynomials?

Combine like terms, which means adding the coefficients of terms that have the same degree.

What is the easiest way to subtract polynomials?

Change subtraction to addition by flipping the signs of the polynomial being subtracted.

What is the process to multiply polynomials?

Multiply every term of the first polynomial by every term of the second polynomial.

What is FOIL used for?

FOIL is used to multiply two binomials (two terms by two terms), standing for First, Outer, Inner, and Last.

How do you factor a polynomial?

To factor a polynomial, you need to find two numbers that add to the coefficient of the middle term and multiply to the constant term.

What happens to polynomials with negative coefficients?

The same factoring process applies, but you must carefully track signs while adding and multiplying.

What is the difference of squares?

The difference of squares is a specific pattern where a squared term is subtracted from another squared term, factoring into (a + b)(a - b).

What is a sum of cubes formula?

For a cubed plus b cubed, it factors as (a + b)(a² - ab + b²).

What should you do with a polynomial to check if it can be factored?

Look for patterns in sums and differences of squares or cubes, and use organization to factor systematically.

What is a common mistake made when factoring polynomials?

A common mistake is to cancel terms instead of factors, forgetting to properly factor polynomials first.