FP10.5
Demonstrate understanding of the multiplication and factoring of polynomial expressions (concretely, pictorially, and symbolically) including:
  • multiplying of monomials, binomials, and trinomials
  • common factors
  • trinomial factoring
  • relating multiplication and factoring of polynomials.

[C, CN, R, V]

Indicators for this outcome
(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.

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R053238
Pearson Foundations and Pre-calculus Mathematics 10. Student Edition(WNCP ed.)
The student text encourages the "big ideas" approach to develop concepts on what is important to think, do and understand. The teaching for understanding instructional approach develops deeper understanding of the concepts. Each chapter in the student text includes checkpoints, a study guide, a review, a practice test and a project.
•  Pearson Foundations and Pre-calculus Mathematics 10. Teacher Resource with CD
Media and Formats : Book
Price : $100.01
Record posted/updated: August 13, 2019