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The Quadratic Formula
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Multiplication by 111
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Solving Linear Systems of Equations by Elimination
Rationalizing the Denominator
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Factoring Trinomials
Linear Relations and Functions
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Axis of Symmetry and Vertices
Equations Quadratic in Form
The Appearance of a Polynomial Equation
Subtracting Reverses
Non-Linear Equations
Exponents and Order of Operations
Factoring Trinomials by Grouping
Factoring Trinomials of the Type ax 2 + bx + c
The Distance Formula
Invariants Under Rotation
Multiplying and Dividing Monomials
Solving a System of Three Linear Equations by Elimination
Multiplication by 25
Powers of i
Solving Quadratic and Polynomial Equations
Slope-intercept Form for the Equation of a Line
Equations of Lines
Square Roots
Integral Exponents
Product Rule for Radicals
Solving Compound Linear Inequalities
Axis of Symmetry and Vertices
Multiplying Rational Expressions
Reducing Rational Expressions
Properties of Negative Exponents
Fractions
Numbers, Factors, and Reducing Fractions to Lowest Terms
Solving Quadratic Equations
Factoring Completely General Quadratic Trinomials
Solving a Formula for a Given Variable
Factoring Polynomials
Decimal Numbers and Fractions
Multiplication Properties of Exponents
Multiplying Fractions
Multiplication by 50


 
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Definition of Factoring a Polynomial

To factor means to write a quantity or an expression as a product.

To factor a whole number, such as 12, we write it as a product of whole numbers. For example:

12 = 2 · 6

12 = 2 · 2 · 3

To factor a polynomial, such as x2 + 5x, means to write it as a product of polynomials: x2 + 5x = x(x + 5).

We say x(x + 5) is the factorization of x2 + 5x.

Multiply Factor

3 · 5

2 · 3 · 3

5x(6x + 7)

(w + 6)(w - 5)

= 15

= 18

= 30x2 + 35x

= w2 + w - 30

15

18

30x2 + 35x

w2 + w - 30

= 3 · 5

= 2 · 3 · 3

= 5x(6x + 7)

= (w + 6)(w - 5)