Factoring Polyomials

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Grade 9: The Learning Equation Math

22.13 Factoring Polynomials

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Variables and Equations

Refresher pp 56-7

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Prerequisite Skills:

Explain and apply the exponent laws for powers with integral exponents.

Perform the operations of addition and subtraction on polynomial expressions.

Find the product of two monomials, a monomial and a polynomial, and two binomials.

Find the quotient when a polynomial is divided by a monomial.

use rectangular tile models to factor second-degree binomials and trinomials

greatest common factor (GCF), inspection, polynomial, like terms, quotient, numerical coefficient

Learning Outcomes: Review Enrichment Key Terms Prerequisite Skills

The student will:

Factor trinomials using common factors.

Vocabulary
Vocabulary and ("translation")	Example(s)/Translation	Explanation
common factor	2 is a common factor of 6 and 12	For numbers: a number that divides into two or more numbers without a remainder
common factor	3x is a factor of: 18x⁴ - 6x³ + 12x²	For polynomial: a term that divides into all of the terms of the polynomial without a remainder
greatest common factor (GCF)	6 is the GCF of 6 and 12	For numbers: the greatest number that divides into two or more numbers without a remainder
	x is the GCF of x² + 2x	For polynomial: the largest term that divides into all of the terms of the polynomial without a remainder
	6x² is the GCF of: 18x⁴ - 6x³ + 12x²

Quia - Matching - Grade 9 Algebra Vocabulary

GCF Example:	x²+2x	3x²-12x	18x⁴ - 6x³ + 12x²
Format Change to enter into many computer programs xⁿ to x^n	x^2+2x	3x^2-12x	18x^{^}4 - 6x^{^}3 + 12x^{^}2
Factor:	= x(x+2)	= 3x(x-4)	=6x²(3x² - x + 2)
GCF	x	3x	6x²

Factor trinomials using the sum and product method.

Factoring trinomials with and without Algebra tiles

Three examples are provided in the first section. Expressions are randomly generated in the other sections. Virtual algebra tiles are provided for the questions where expressions are generated. Factor the expression following the steps provided in the examples. The steps for the "sum and product" method are available on the right side of the screen for each randomly generated expression.

Now we need to be able to enter our own trinomials, complete the work and check the answer. You can generate additional trinomials or input your own to check your work.

Review Learning Outcomes Enrichment Key Terms Prerequisite Skills

Quia - Concentration - Grade 9 Algebra Vocabulary

Look at four different types of trinomials we need to learn how to factor.

x^2 + bx + c

natural numbers

integers

This is the first of four types of trinomials to factor.

x² + bx + c

b = sum number c = product number

Hint 1:

Hint 2:

1. Click on "Show a Problem".
2. Do the problem mentally or on paper.
3. Hint 1: Use the product number "c" to determine all of the possible factors.
4. Hint 2: Use the sum number "b" determines which pair of factors is correct.
5. Click "Show the Answer" to check your work.
6. Repeat until you can do the problems easily.