- multiplying of monomials, binomials, and trinomials
- common factors
- trinomial factoring
- relating multiplication and factoring of polynomials.
[C, CN, R, V]
| (It is intended that the emphasis of this outcome be on binomial by binomial multiplication, with extension to polynomial by polynomial to establish a general pattern for multiplication.) | |
| (a) |
Develop, generalize, explain, and apply a strategy of symbolic manipulation to determine the product of two binomials by analyzing concrete and pictorial models. |
| (b) |
Explain the relationship between the multiplication of two binomial expressions and the area of a rectangular region. |
| (c) |
Develop (concretely, pictorially, or symbolically), explain, and apply understanding of how multiplication of binomials is related to the multiplication of two-digit numbers. E.g. use algebra tiles and base ten blocks to compare and relate the products of $(x + 1)(3x + 2)$ and $(11)(32)$. |
| (d) |
Develop, generalize, explain, and apply a strategy for multiplying polynomials. |
| (e) |
Analyze the multiplication of two polynomials for errors and explain the strategy used. |
| (f) |
Explain why evaluating at a value for the variable in a product of polynomials in factored form should give the same solution as evaluating the expanded and simplified form of the polynomial product at the same value. E.g. explain why $x^2 + 5x + 6$ should have the same value as $(x + 3)(x + 2)$ when evaluated at $x = -4$. |
| (g) |
Explain, using concrete or visual models, how the processes of factoring and multiplication are related. |
| (h) |
Develop (using concrete materials, pictures, or visualization), generalize, explain, and apply strategies for factoring and verifying the factors of binomials, including numerical binomial expressions. E.g. $32 + 20 = 4(8 + 5)$. |
| (i) |
Sort a set of polynomials according to the type(s) of factoring that could be applied to them. |
| (j) |
Explain and apply strategies for determining whether given factors are those of a given polynomial. |
| (k) |
Develop, generalize, explain, and apply strategies for factoring a trinomial. |
| (l) |
Critique the statement “any trinomial can be factored into two binomial factors”. |
| (m) |
Explain how differences of squares can be factored using trinomial factoring strategies. |
| (n) |
Explain why it is important to look for common factors first when factoring a trinomial. |
