Notes on factoring
Theory of Factoring
Factoring uses rules to reduce an Algebraic expressions with add and subtracts operators into anequivalent where the expression are multiply and divide operators.
4.2 How do we use factoring in Algebra?When an algebraic expression is divided up into factors we can use the zero factor property to solvethe expression.
4.3 Zero factor property processBasically if A*B=0 than either A or B or both have to be zero. Then we can set both factors equalto zero and solve. Note that if an equation equal zero we are graphically solving the point intersectswith the x-axis.Fpr instance ifax2+bx+c= 0 in its general form we can solve for the equation for x.Ifax2+bx+c=yofy=ax2+bx+c=ythen we are considering the equation and we can plotthe equation on a TI-73 or equivalent calculator or on a program like geometers sketchpad.
4.4 An example of a specific trinomial equationx2+ 4x+ 4 = 0 when factored = (x−2)(x−2) = 0 settingx−2 = 0, x= 2andx−2 = 0, x= 2)the solutions arex= 2,2 therefore both solutions arex= 2 wheny= 0 so the parabola describedbyx2+ 4x+ 4 = 0
4.5 conclusionThe equation graphs asy=x2+ 4x+ 4 When we sety= 0 then 0 =x2+ 4x+ 4 orx2+ 4x+ 4 = 0.By definition when the value ofy= 0 and a value of x shows where the curve touches or crosses thex or -x axis.
4.6 Factoring MethodsFactoring has rules that are followed to solving an algebraic problem.1
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