A1.A.3.3 Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1.
In a Nutshell
Students will factor polynomial expressions, including quadratics. They will factor out the greatest common factor from polynomials of any degree and factor quadratics with a lead coefficient of one into two binomials.
Student Actions

Teacher Actions


Students will develop accurate and appropriate procedural fluency by finding the factors of a polynomial expression or quadratic equation.

Students will develop a deep and flexible conceptual understanding by comparing the quadratic equations and their graphs to see that the factors are solutions called xintercepts (zeros) of the graphed equation.
 Students will develop mathematical reasoning when they observe and explain how factoring is the reverse of distributing.


Use and connect mathematical representations by helping students discover the relationships between quadratic equations and their graphs, including those that model realworld situations.

Pose purposeful questions that guide students toward discovering factors of expressions.
 Implement tasks that promote reasoning and problem solving by guiding students to interpret the mathematical relationship in the original context of the problem algebraically

Key Understandings

Misconceptions



Students may forget to factor the greatest value possible from an expression before beginning to factor the polynomial.

Students may not take the realworld context for a quadratic relationship into account when giving solutions, causing them to include solutions that would not fit the situation.

Students may not identify the correct sign of the factors involved.

OKMath Framework Introduction
Algebra 1 Introduction
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