In Chapter 5, I learned about Polynomial Operations

Lesson 1 was review and a preview into the chapter. We reviewed what a variable and what an algebraic expression is. We also learned the difference between a monomial, binomial, trinomial, and a polynomial. (shown in image). With these polynomials, you can classify them by degree. “The degree of a monomial is the sum of the exponents of its variable(s)”  and “the degree of a polynomial is the degree of the term with the highest degree.” After we learned how degrees work, we started to add and subtract polynomials. At first, with algebra tiles, then, just algebraically.

Lesson 2 taught us how to multiply a polynomial by a monomial. Again, we used algebra tiles at first but then we learned how to expand an expression using the distributive property. The distributive property is a(b+c) = ab +ac. (examples shown in image below).

In lesson 3, We expanded on what we knew and learned how to multiply two binomials together. In this lesson, there were two models, algebra tiles and an area diagram, however I prefer to solve algebraically. Again, we expanded on the distributive property concept. The distributive property for two binomials is as follows: (a+b)(c+d) = a (c+d) b (c+d)= ac +ad +bc +bd.

I learned to use the acronym FOIL to help remember which terms to multiply first

F- First term in each bracket

O- Outside terms

I- Inside terms

L- Last terms in each bracket

In lesson 4, we practised the FOIL method and multiplied polynomials together. This continued in Lesson 5, and we were introduced problem solving by multiplication of polynomials and went more in depth with this in lesson 6.