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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
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.
Factor 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.
For example, suppose you were trying to factor
As another example, suppose you were trying to solve
Assign just this concept or entire chapters to your class for free.
Key Term Reference
 equation
 Appears in these related concepts: A General Approach, Equations and Inequalities, and What is an Equation?
 expression
 Appears in these related concepts: Compound Inequalities, Sets of Numbers, and Graphs of Equations as Graphs of Solutions
 factor
 Appears in these related concepts: Rational Algebraic Expressions, Finding Factors of Polynomials, and Factors
 quadratic
 Appears in these related concepts: Stretching and Shrinking, The Discriminant, and What is a Quadratic Function?
 quadratic equation
 Appears in these related concepts: Graphing Quadratic Equations In Standard Form, Completing the Square, and Linear and Quadratic Equations
 root
 Appears in these related concepts: Newton's Method, Rational Exponents, and Introduction to Radicals
 square
 Appears in these related concepts: Factoring a Difference of Squares, Radical Equations, and Matrix Multiplication
 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, 20 Jun. 2016. Retrieved 28 Jul. 2016 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/quadraticfunctionsandfactoring6/factoring45/factoringperfectsquaretrinomials725876/