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 Pre-algebra Arithmetics Integers Divisibility Decimals Fractions Exponents Percentages Proportional reasoning Radical expressions Graphs Algebra Monomials Polynomials Factoring Linear Equations Graphs of linear equations Rectangular Coordinate System Midpoint Formula Definition of Slope Positive and negative slope Determine the slope of a line Equations of lines Equation of lines (from graph) Applications of linear equations Inequalities Quadratic equations Graphs of quadratic equations Absolute Value Radical expressions Exponential equations Logarithmic equations System of equations Graphs and functions Plotting points and naming quadrants Interpreting Graphs Relations and Functions Function Notation Writing a Linear Equation from a Table Writing a Linear Equation to describe a Graph Direct Variation Indirect Variation Domain and range Sequences and series Matrices Inverse of a matrix Determinants Inner product Geometry Triangles Polygons 2-D Shapes 3-D Shapes Areas Volume Pythagorean Theorem Angles Building Blocks Geometry Transformations Parallel, coincident and intersepting lines Distances in the plane Lines in space Plane in space Angles in the space Distances in the space Similarity Precalculus Sequences and series Graphs Graphs Definition of slope Positive or negative slope Determine the slope of a line Equation of a line (slope-intercept form) Equation of a line (point slope form) Equation of a line from graph Domain and range Quadratic function Limits (approaches a constant) Limits (approaches infinity) Asymptotes Continuity and discontinuities Parallel, coincident and intersepting lines Introduction to Functions Limits Continuity Asymptotes Trigonometry Trigonometric ratios The reciprocal trigonometric ratios Trigonometric ratios of related angles Trigonometric identities Solving right angles Law of sines Law of cosines Domain of trigonometric functions Statistics Mean Median Mode Quartiles Deciles Percentiles Mean deviation Variance Standard Deviation Coefficient of variation Skewness kurtosis Frequency distribution Graphing statistics & Data Factorial Variations without repetition Variations with repetition Permutations without repetition Permutation with repetition Circular permutation Binomial coefficient Combinations without repetition Combinations with repetition

Factoring
Factoring trinomials x2+bx+c

To factor a trinomial in the form x2+bx+c, you have only to remember that:

x2+bx+c=(x+a)(x+b)=x2+ax+bx+ab=x2+(a+b)x+ab

The coefficient of the middle term is the sum of a and b.
The last term is the product of a and b.

Therefore, to factor a trinomial in which the coefficient of x2 is 1, we need only find the numbers a and b whose sum is the coefficient of the middle term and whose product is the constant term (last term).

Factor x2+12x+20
We need two numbers whose sum is 12 and whose product is 20.
Here are all the possibilities for products that are 20:

 Product Sum 1·20=20 1+20=21 2·10=20 2+10=12 4·5=20 4+5=9

The second line gives us what we want.
The factors of x2+12x+20 are (x+2) and (x+10):

x2+12x+20=(x+2)(x+10)

Factor m2-7m+10
We need two numbers whose sum is -7 and whose product is 10. Therefore, we are looking for two negative numbers.
Here are all the possibilities for products that are 10:

 Product Sum (-1)·(-10)=10 -1-10=-11 (-2)·(-5)=10 -2-5=-7

The second line gives us what we want.
The factors of m2-7m+10 are (x-2) and (x-5):

m2-7m+10=(x-2)(x-5)