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FOIL Method
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Addition Property of Equality
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Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
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Factoring The Difference of 2 Squares
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Using Patterns to Multiply Two Binomials
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Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
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Composition of Functions
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Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
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Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
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Adding Fractions
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Functions and Graphs
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Multiplying and Dividing Fractions 1
Composition of Functions
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Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
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Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
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Angles and Degree Measure
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Factoring Trinomials

We can also use trial and error to try to factor a trinomial. In this method, we make educated guesses about the factors. Then we multiply to see if one of the guesses is correct.

Factor by trial and error: 5x2 - 22x + 8


Since the first term of the trinomial is 5x2, the product of the first terms of the binomials is 5x2. Therefore, it is reasonable to guess that the first terms are 5x and 1x.

Thus, 5x2 - 22x + 8 = (5x + ?)(1x + ?)

Because the last term of the trinomial is 8, the product of the last terms of each binomial must also be 8. The possible pairs of integers whose product is 8 are 8 · 1, 4 · 2, -8 · (-1), and -4 · (-2).

Since the last term of 5x2 - 22x + 8 is positive and the middle term is negative, we need only check the negative integer factors of 8.

We can use the FOIL method to check each possibility.

Pissibilities F O I L Resulting trinomial
(5x - 8)(1x - 1)

(5x - 4)(1x - 2)

(5x - 1)(1x - 8)

(5x - 2)(1x - 4)

 = 5x2 - 5x - 8x + 8

= 5x2 - 10x - 4x + 8

= 5x2 - 40x - 1x + 8

= 5x2 - 20x - 2x + 8

= 5x2 - 13x + 8

= 5x2 - 14x + 8

= 5x2 - 41x + 8

= 5x2 - 22x + 8


The last guess yields the correct middle term, -22x.

So, the factorization is (5x - 2)(x - 4).

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