2Objectives Common Factors Factoring and Equations Factoring by Grouping
3Common FactorsWhen factoring a polynomial, we first look for factors that are common to each term. By applying the distributive property, we can write a polynomial as two factors.For example:It can be factored as follows:
9Example Solve each polynomial equation. a. b. Solution a. We begin by factoring out the greatest common factor.b. We begin by factoring out the greatest common factor.No real number can satisfy x2 = –1, the only solution is 0.
10Polynomial equations can also be solved numerically and graphically.
12ExampleSolve the equation 6x – x2 = 0 numerically, graphically, and symbolically.SolutionNumerical: Make a table of values.xy1715283946Graphical: Plot the points in the table.The intercepts are the solution to the equation.
13Example (cont)Solve the equation 6x – x2 = 0 numerically, graphically, and symbolically. Solution Symbolic: Start by factoring the left side of the equation.Note that the numerical and graphical solutions agree with the symbolic solutions.