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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

 Polynomials Polynomial Vocabulary Simplifying expressions Addition Subtraction Multiplication (FOIL) Multiplication Special products Long division Synthetic division Remainder theorem Roots and factors of a polynomial Polynomial Function Roots and factors of a polynomial Let P(x) be a polynomial. A number a such that P(a)=0 is called a root or zero of P. If x=a is a root of a polynomial, then x-a is a factor of that polynomial. Consider the polynomial P(x)=x2+2x-3. Let's plug x=1 into the polynomial: p(1)=12+2·1-3=0. Consequently x=1 is a root of the polynomial P(x)=x2+2x-3. Note that x-1 is a factor of the polynomial P(x)=x2+2x-3. The fundamental theorem of algebra stated that a polynomial P(x) of degree n has n roots, some of which may be degenerate. What are the possible integer roots of P(x)=2x5 -3x3 +4x2 -9x + 6 ? If there are integer roots, they will be factors of the constant term 6; namely 1, -1, 2, -1, 3, -2, 6, -6. Now, is 1 a root? To answer, we will divide the polynomial by x-1 and hope for remainder 0. Yes! 1 is a root! Now, is 1 a root again? To answer, we divide the resulting polynomial by x-1 and hope for remainder 0. Yes! 1 is a root again!. Now, is -2 a root? Yes! -2 is a root! We have: 2x5 -3x3 +4x2 -9x + 6 =(x-1)2(x+2)(2x2 +3)where 2x2 +3 does not have integer roots. Conclude that the integer roots of P(x)=2x5 -3x3 +4x2 -9x + 6 are a=1, b=1 and c=-2 What are the possible integer roots of this polynomial? $\fs2P(x)=-3x^3-18x^2-27x$          Roots a= b= c=