Specific Outcome: It is expected that students will:
[CN, R, V]
Prior knowledge from previous grade levels includes:
It is important that students are able to provide explanations for the restrictions on the variables in the definitions and exponent laws in Achievement Indicators 3.1, 3.2 and 3.3. In particular, in Achievement Indicator 3.2, students are expected to explain when a ≥ 0:
Students are not required to represent the product of two trinomials concretely or pictorially.
Students are expected to perform operations on polynomials involving one or two variables.
Students, from Kindergarten to Grade 9, have been encouraged to develop personal strategies for performing operations with numbers. In Achievement Indicator 4.3, students are therefore expected to explain the strategy they used for multiplying two-digit numbers; e.g., 15 × 23 = (10 + 5) (20 + 3).
Division of a polynomial by a binomial is not part of this outcome and will be introduced in Mathematics 30-1.
Achievement Indicators |
Acceptable Standard |
Standard of Excellence |
| 2.4.1 Model the multiplication of two given binomials, concretely or pictorially, and record the process symbolically. | ** | |
| 2.4.2 Relate the multiplication of two binomial expressions to an area model. | ** | |
| 2.4.3 Explain, using examples, the relationship between the multiplication of binomials and the multiplication to two-digit numbers. | ** | |
| 2.4.4 Verify a polynomial product by substituting numbers for variables. | ** | |
| 2.4.5 Multiply two polynomials symbolically, and combine like terms in the product. | ** | |
| 2.4.6 Generalize and explain a strategy for multiplication of polynomials. | ** | |
| 2.4.7 Identify and explain errors in a solution for a polynomial multiplication. | Identify errors in a solution. | Identify and explain errors in a solution. |
Specific Outcome: It is expected that students will:
[C, CN, R, V]
Topic: Algebra and Number, Specific Outcome 1 should be completed prior to this outcome.
Students are expected to demonstrate their understanding of factoring concretely, pictorially and symbolically. Concrete and pictorial representations should be limited to trinomials of the form ax2 + bx + c, where a ∈I.
Students are expected to factor expressions such as ax2 + bx + c, where a ∈I.
In Achievement Indicator 5.1, if the common factor is a monomial, students are expected to factor the remaining polynomial factor.
Polynomials involving two variables, e.g., ax2 + bxy + cy2, are included in this outcome.
Students should not spend a lot of time factoring quadratics in which the product ac has many factors.
Students are not expected to factor such expressions as af2 + bf + c, where f is itself a monomial or a binomial.
Students are expected to have a good understanding of, and mastery of the processes involved in, factoring polynomials since factoring is essential for topics in both Mathematics 20-1 and 20-2.
Achievement Indicators |
Acceptable Standard |
Standard of Excellence |
| 2.5.1 Determine the common factors in the terms of a polynomial, and express the polynomial in factored form. | ** | |
| 2.5.2 Model the factoring of a trinomial, concretely or pictorially, and record the process symbolically. | ** | |
| 2.5.3 Factor a polynomial that is a difference of squares, and explain why it is a special case of trinomial factoring where b = 0 . | Factor without explanation. | Factor with a complete explanation. |
| 2.5.4 Identify and explain errors in a polynomial factorization. | Identify errors without explanation. | Factor with a complete explanation. |
| 2.5.5 Factor a polynomial, and verify by multiplying the factors. | ** | |
| 2.5.6 Explain, using examples, the relationship between multiplication and factoring of polynomials. | ** | |
| 2.5.7 Generalize and explain strategies used to factor a trinomial. | ** | |
| 2.5.8 Express a polynomial as a product of its factors. | ** |
A single term with coefficients and/or variables
For example: 5x2; 2 ; x3y
A sum of multiple monomials
A sum of multiple terms
For example: x + 5 ; 2x ; 2a3 + 7ab + b 2
A polynomial with two monomials
A sum of two terms
For example: x + 5 ; 2x - 3 ; 2a3 - 6ab + b 2
A polynomial with three terms
A sum of three monomials
For example: x2 + 6x + 5 ; 2x - y + 3z ; 2a3 -4b + b2
Distributive Property
The rule that states a(b + c) = ab + ac
A polynomial with three terms
a number that can only be divided by one and itself
breaking a number down into its prime factors
The largest factor shared by two or more terms
For example the GCF of 12 and 28 is 4
The smallest multiple shared by two or more terms
Multiples of 6 and 8 are 24, 48, 72 ... The LCM is 24.
Difference of squares
An expression of the form a2 - b2 that involves the subtraction of two squares
Perfect square trinomial
The trinomial is of the form (ax)2 + 2abx + b2 or (ax)2 - 2abx + b2