Operations with Monomials and Polynomials: Adding, Subtracting, Multiplying, and Dividing.

Fantastic lesson that tackles the many times taught topic of operations with polynomials. What is the degree of a polynomial? ... How do I apply FOIL? Vertical multiplication is confusing! ... and many more headaches.

You won't have to worry anymore for all of this. This lesson uses a concrete to abstract approach, that capitalizes in your previous basic knowledge of calculating the area of a rectangle, and the volume of a cube to model you the multiplications of binomials and polynomials. Nevertheless, it is important to point out that the vocabulary provided at the bottom section of the webpage, while boring and monotonous would help to pave the way of a better understanding of the concepts taught inside the lesson relying on your visual side. Use your finger or your stylus to pull down the MARKER TOOLS menu at the upper right section of the screen and try to capitalize on the highlighter and pen to mark important sections or write reminders to go back using the navigability provided by the thumbnails at the left of the screen. You will be really impressed by the easiness of the lesson! Accept the challenge!

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

Algebraic expression: A given set of letters called variables, and real numbers called constants that are combined using addition, subtraction, multiplication, division and/or exponentiation.

Associative Property: Grouping addends in a sum or factors in a product in different order does not affect the answer.

Binomial: Expression that has two (bi) terms.

Commutative Property: Modifying the order of addends or factors in a expression does not affect the sum or product.
Order is not important when adding or multiplying.

Constant: It is a number or value that remains always the same. Never changes.

Difference of two squares: a2 - b2 = (a +b)(a - b)

Exponent: It is a raised number representing the repeated multiplication of a given factor.

Perfect square trinomial: A trinomial generated by the product of two equal binomials.

Expression: Any combination of numbers and operations without the = sign.

Factoring: The process to brake a polynomial down into the product of several factors.

Factors: All whole numbers that are multiplied together to yield another number.

Factored Form: Any polynomial that is written as the product of polynomials of lower degree that may be obtained from the original polynomial.

Like terms: Terms that have the same combination of variables to the same power as factors.

Operation: Any action we perform on one or two numbers to produce a new number. Most common ones are addition, subtraction, multiplication, division, square roots, powers, and so on.

Polynomial: A algebraic statement with one or more terms. Word comes from “poly” which means many.

Polynomial (third degree): Geometric representation. A third degree polynomial may be represented as the volume of a rectangular prism for which length, width and depth are the linear factors of the polynomial.

Power: Exponent of a number or variable.

Subtraction: Adding the opposite.

Synthetic division: A process of dividing a polynomial by a linear factor, using the coefficients and ignoring the variable and the exponents (they are relevant just as the position to place the coefficients). When dividing the sign of the divisor is reversed to avoid subtracting and to allow just to add.

Term: A form of grouping one or more numerical and/or variable factors by means of multiplication and division. Addition and subtraction symbols separate terms.

Variable: A letter used to represent a number. When the variable is part of an equation, it is possible to find the value for which it stands for by solving the equation. This is the solution (s) of the equation.

Variable expression: Mathematical phrase with at least one variable in it.


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