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Factoring Trinomials of the Form ax^2 + bx + c; Perfect Squares
The polynomial $ax^2 + bx + c$ can be factored using a variety of methods, including trial and error.
Learning Objectives

Differentiate between perfect square trinomials and nonperfect square trinomials

Apply factoring techniques to factor a trinomial of the form ax2 + bx + c
Key Points

Some trinomials, known as perfect square trinomials, can be factored into two equal binomials.

We can factor
$a^2 b^2$ , the difference of two squares, by finding the terms that produce the perfect squares and substituting these quantities into the factorization form. When using real numbers, there is no factored form for the sum of two squares. 
Perfect square trinomials factor as the square of a binomial. To recognize them, look for whether (1) the first and last terms are perfect squares, and (2) the middle term is divisible by 2, and when halved, equals the product of the terms that when squared produce the first and last terms.
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
Factoring Trinomials
The polynomial
Ultimately, the trinomial should be factored in the form
Perfect Squares
Some trinomials, known as perfect square trinomials, can be factored into two equal binomials. For example:
and
Perfect square trinomials always factor as the square of a binomial.
To recognize a perfect square trinomial, look for the following features:
 The first and last terms are perfect squares.
 The middle term is divisible by 2.
For example,
Given that the coefficient of x^{2} is 1, we know that the factored form will be
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Key Term Reference
 coefficient
 Appears in this related concepts: The Equilibrium Constant, Balancing Chemical Equations, and The Quadratic Formula
 constant
 Appears in this related concepts: Combined Variation, Quadratic Functions of the Form f(x) = a(xh)^2 + k, and Direct Variation
 factor
 Appears in this related concepts: The Perceptual Process, Finding Factors of Polynomials, and Solving Quadratic Equations by Factoring
 factorization
 Appears in this related concepts: Trinomials of the Form ax^2 + bx + c, Where a is Not Equal to 1, Partial Fractions, and Greatest Common Factor and Factoring by Grouping
 polynomial
 Appears in this related concepts: Linear and Quadratic Functions, The Remainder Theorem and Synthetic Division, and Polynomials: Introduction, Addition, and Subtraction
 real number
 Appears in this related concepts: Real Numbers, Functions, and Graphs, Intermediate Value Theorem, and Solving Problems with Inequalities
 real numbers
 Appears in this related concepts: Finding Domains of Functions, Piecewise Functions, and Linear Inequalities
 square
 Appears in this related concepts: Special Factorizations and Binomials, Radical Equations, and Matrix Multiplication
 term
 Appears in this related concepts: Basics of Graphing Polynomial Functions, The 22nd Amendment, and Democracy
 variable
 Appears in this related concepts: Related Rates, Calculating the NPV, and Fundamentals of Statistics
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Source: Boundless. “Factoring Trinomials of the Form ax^2 + bx + c; Perfect Squares.” Boundless Algebra. Boundless, 25 Jan. 2015. Retrieved 26 May. 2015 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/thebuildingblocksofalgebra1/factoring12/factoringtrinomialsoftheformax2bxcperfectsquares725876/