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GUIDED NOTES – Lesson 2-4 Factoring Quadratic Functions Name: ______________________ Period: ___ Objective: I can factor and solve quadratic functions using GCF, difference of squares, grouping, bottoms up.Another method for solving quadratic functions (what value(s) for x will give us 0), is to factor. Let’s start with a review of basic factoring techniques. First we need to be able to pull out the GREATEST COMMON FACTOR (GCF) from a function/expression. This is the combination of the largest number and variable combination that can be factored from every term in the expression.a) 3x + 9b) 15x + 25x2c) x4 – 7x2d) 9x3 + 18x2e) 2x3 – 4x2 + 8The DIFFERENCE OF PERFECT SQUARES applies to quadratics that contain perfect square terms. They follow a factorable pattern of (a + b)(a – b).a) x2 – 64b) x2 – 144c) 16x2 – 81d) 100x2 – 9y2Notice there is no b term in standard form, because it has been cancelled out.PRODUCT/SUM FACTORING works on trinomials where a = ____. Find two terms which multiply to the third term and add to the second term.a) x2 + 8x + 15b) x2 – 11x + 30c) x2 – 8x – 9 d) x2 + 3x – 18BOTTOMS UP FACTORING is a method to use for trinomials where a is ___________________.3688715681516x2 + 11x + 4006x2 + 11x + 45786120134970057942131110500Factor out GCF (if there is one)Multiply first and last numbersFind two numbers that multiply to the product and add to the middle termWrite two factors as fractions over a term.Reduce fractionsKick denominator to front (“bottoms up”)02368555x2 – 17x + 12005x2 – 17x + 123611437387352x2 – x – 1002x2 – x – 1Now for SOLVING QUADRATICS USING FACTORING… the point of doing all the factoring methods above is to ultimately solve a quadratic function using factoring. Remember that the solution is found by setting the function equal to _____, so we can get our x-intercepts which are our solutions, aka ___________ aka ____________.The zero-product property rule tells u that if the product of two numbers is zero, then one of them must be zero. If ab = 0, then either a = 0, b = 0 or both a and b = 0. So if we factor a quadratic and get (x + 3)(x – 5) = 0, then the solutions are x = _____ and x = _____, both cause the function to equal 0.a) x2 – 25 = 0b) x2 – x = 12c) 3x2 + 2x – 21 = 0Solutions:Solutions:Solutions:You can graph these functions in your calculator and indeed see that the solutions are the x-intercepts of the graph. ................
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