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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 by grouping Not all polynomials have a common factor in each term. In this case, they may sometimes by factored by grouping. Factoring by grouping can be attempted on any polynomial with four or more terms. However, not every such polynomial can be factored in this way. To factor a polynomial by grouping Groups the terms of the polynomial so that the first two terms have a common factor and the last two terms have a common factor. Factor out the common factor from each group. Factor out the resulting common binomial factor. If there is no common binomial factor, regroup the terms of the polynomial and repeat steps 2 and 3. Factor x3+6x2+x+6 Since the terms of the polynomial do not have a common factor (other than 1), the only option is to attempt to factor this polynomial by grouping. The first two terms, x2 and 6x2, have a common factor of x2. The only common factor of the last two terms, x and 6, is 1. We are going to: 1. Factor out x2 from x3+6x2 2. Factor out 1 from x+6 3. Factor out the common binomial factor, x+6. x3+6x2+x+6 = x2(x+6)+1(x+6) = (x+6) (x2+1) Factor 12x3-9x2+20x-15 12x3-9x2+20x-15 = 3x2(4x-3)+5(4x-3) = (4x-3) (3x2+5)