Presentation on theme: "Basic Factoring of Polynomials"— Presentation transcript:
1 Basic Factoring of Polynomials Brought to you byTutorial Services – The Math Center
2 Solving Quadratic Polynomials Three steps to solving quadratic polynomialsSolve by factoringSolve by using the square root propertySolve by using the quadratic equation
3 Quadratic Polynomials How does one isolate ‘x’ in a case like the following?It is unnecessarily difficult.Therefore, other methods must be used.
4 Quadratic factoring Example: First we need to… MAKE THE EQUATION EQUAL TO ZEROSo:This polynomial can be factored by considering the following:The polynomial has three termsFirst, Middle, and Lastz2 + 4z + 4z2 + 4z + 4 = 0
5 Quadratic factoring (Cont.) The first term is z2The Middle term is 4zThe Last terms is 4To factor, the best way to start is to place the parenthesis for factoring:( F L ) ( F L )The F * F must equal the first term.The L * L must equal the last term.
6 Quadratic factoring (Cont.) The inner plus the outer must equal the middle term.z * z = z2 First Term2z + 2z = 4z Middle Term2 * 2 = 4 Last Term
7 Quadratic factoring (Cont.) In summary:( F L ) ( F L )F * F = First termL * L = Last TermInner + Outer = Middle Term
9 Quadratic EquationA quadratic function can also be solved by the quadratic formula:It must be in standard form:Ax2 + Bx + C = 0
10 Cubic PolynomialsThese polynomials can be solved by using the synthetic division or if possible, by factoring.Only factoring will be considered
11 Some polynomials can be grouped to factor the like terms. By FactoringSome polynomials can be grouped to factor the like terms.x3 + 2x2 + 2x + 4 = 0Example:First: Group the terms(x3 + 2x2) + (2x + 4) = 0Second: Factor out common termsx2 (x + 2) + 2 (x + 2) = 0Third: Factor the (x + 2) termAnswer: (x2 + 2)(x + 2) = 0
12 SUMMARY Polynomials can be of various degrees; the most popular are: LinearQuadraticCubicFactoring is a tool to help solve for a variable.In order to solve by factoring it is necessary to MAKE THE EQUATION EQUAL TO ZERO.
13 Tutorial Services – The Math Center Brought to you byTutorial Services – The Math CenterQuestions?
14 Links and Handouts Working with Polynomials Worksheet Factoring Polynomials HandoutCompleting the Square HandoutAlgebra and Logarithmic Functions HandoutPolynomial QuizWorking with Polynomials Quiz