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Factoring Perfect Square Trinomials
When a trinomial is a perfect square, it can be factored into two equal binomials.
Learning Objective

Evaluate whether a quadratic equation is a perfect square and factor it accordingly if it is
Key Points
 Some quadratics, known as perfect squares, can be factored into two equal binomials.
 Perfect squares have the form
$a^2+2ab+b^2$ .  Perfect square quadratics have only one root.
Terms

trinomial
A polynomial expression consisting of three terms, or monomials, separated by addition and/or subtraction symbols.

binomial
A polynomial consisting of two terms, or monomials, separated by addition or subtraction symbols.
Full Text
Recognizing Perfect Square Trinomials
Note that if a binomial of the form
For example, if the expression
It is important to be able to recognize such trinomials, so that they can the be factored as a perfect square.
Factoring Perfect Square Trinomials
If you are attempting to to factor a trinomial and realize that it is a perfect square, the factoring becomes much easier to do.
Example 1
Suppose you were trying to factor
Example 2
Suppose you were trying to solve
Thus the original equation has the form
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Key Term Reference
 equation
 Appears in these related concepts: A General Approach, Equations and Inequalities, and Graphs of Equations as Graphs of Solutions
 expression
 Appears in these related concepts: Compound Inequalities, Sets of Numbers, and Simplifying, Multiplying, and Dividing
 factor
 Appears in these related concepts: Factors, Solving Quadratic Equations by Factoring, and Finding Factors of Polynomials
 factoring
 Appears in these related concepts: Factoring Accounts Receivable, Rational Algebraic Expressions, and Selling to Consumers
 quadratic
 Appears in these related concepts: What is a Quadratic Function?, The Discriminant, and Stretching and Shrinking
 quadratic equation
 Appears in these related concepts: Linear and Quadratic Equations, Graphing Quadratic Equations In Standard Form, and Completing the Square
 root
 Appears in these related concepts: Introduction to Radicals, The Rule of Signs, and Zeroes of Polynomial Functions with Real Coefficients
 solution
 Appears in these related concepts: Electrolyte and Nonelectrolyte Solutions, Turning Your Claim Into a Thesis Statement, and What is an Equation?
 square
 Appears in these related concepts: Matrix Multiplication, Factoring a Difference of Squares, and Radical Equations
 square root
 Appears in these related concepts: Graphs of Logarithmic Functions, The Quadratic Formula, and Other Equations in Quadratic Form
 term
 Appears in these related concepts: Basics of Graphing Polynomial Functions, The 22nd Amendment, and Introduction to Variables
Sources
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Cite This Source
Source: Boundless. “Factoring Perfect Square Trinomials.” Boundless Algebra. Boundless, 06 Sep. 2016. Retrieved 30 Sep. 2016 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/quadraticfunctionsandfactoring6/factoring45/factoringperfectsquaretrinomials725876/