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Algebra 1
Subject:____________________
Unit Title:
Factoring
5
Unit:_______________________
3 (January 17th –
Quarter:_____________________
March 23rd)
Unit Overview
Unit 5: Factoring
In the last unit algebraic expressions were multiplied to form a new expression that was the product of the factors. The focus of this unit shifts to a
discussion of factoring. When the product is given and the factors are found, this process is called factoring; which is the inverse of multiplying.
Algebraic skills are employed in the factoring process, such as looking for the greatest common factor, recognizing the difference in two squares, and
factoring trinomials of the form ax2 + bx +c.
The use of the zero product property is employed throughout the section on factoring in order to solve factorable quadratic equations. The zero
product property states when the product of two or more numbers is zero, one of those numbers must be zero. An emphasis is placed on the
distinction between factoring an expression and solving an equation.
Math Literacy
Key Vocabulary: factored form, factoring, factoring by grouping, perfect square trinomials, prime factorization, prime polynomial, quadratic
expression, difference of two squares, perfect square trinomial, zero product property, double root.
Supporting Vocabulary: composite number, greatest common factor, prime number
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Common Core State Standard Alignment

ASSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a
difference of squares that can be factored as (x2 – y2)(x2 + y2).

ASSE.3a Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression. Factor a quadratic expression to reveal the zeros of the function it defines.
Sample Essential Questions

Explain the relationship between the multiplication (distribution) of polynomials and factoring.

Explain the difference and similarities among the methods of factoring.

Identify when to use each method for factoring?
Anchor Standards/Central Concepts
11.0 Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor
for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
11.0 Students apply basic factoring techniques to
second- and simple third-degree polynomials.
These techniques include finding a common factor
for all terms in a polynomial, recognizing the
difference of two squares, and recognizing perfect
squares of binomials.
# CST Items
Standard
Learning Targets/
Key Concepts and Skills
2
College-Ready Sample Assessment
Questions

11a I can find the prime factorizing
of monomials.

Factor
16x3 + 20x2 + 20x + 25

11b I can find the greatest common
factors (GCF) of monomials.

Factor
27xy - 81y

11c I can factor trinomials in the
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# CST Items
Standard
Learning Targets/
Key Concepts and Skills
form x2 + bx + c and ax2 + bx +c.

College-Ready Sample Assessment
Questions

11d I can factor a difference of two
squares polynomial.
Determine all values of k that make each
of the following a perfect square.
Explain your reasoning.
4x2 + kx + 1

11e I can factor out the GCF from
polynomials with many terms.

11f I can factor a polynomial
expression by grouping and identify
algebraic properties that are used in
the process.


11g I can use factoring to simplify
expressions (reducing) involving
polynomial division.

11h I can check solution(s) (e.g.
substitution), and reasonableness of
answer.
x2 – 18x + k

x2 + 20 x + k
Create a polynomial that requires at
least two different factoring techniques
to factor completely. Describe
techniques that were used.
Solve the following equations. Check
the solutions.
(d-5)(2d -3) = 0

11i I can solve equations by
factoring using the Zero Product
Property and explain the process of
doing so.
x2 = -7x
(x+3)2 = 3
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Vertical Alignment
 Multiply and divide monomials 7AF2.2

Factor special polynomials 2A4.0
Additional Sample College-Ready Assessments Questions

Sample College-Ready Assessment Questions
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