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Lesson 5-3 Solve by Factoring - Trinomial

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1. Make sure the equation is equal to zero. 2. Factor using the sum and product strategy. 3. Set each factor equal to zero and solve. 4. Write the solution set. You may check your answers using your graphing (or multiview) calculator. Replace the 0 with y, and enter the function into the calculator. Observe where the graph crosses the x-axis, OR look in the table (in the y-column) for the ZEROS. The x-values should be the same as your solutions.

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this is a song by factoring problem so the first thing that you want to do is make sure that the right hand side of the equation equals zero and it doesn't so we're going to move the 40 to The Other Side by attracting so we're going to -40 from this side and -40 from this side noticed that 40 is a constant and we already have a quadratic term and a linear term constant can be added to either of those and so we're just going to write them down like x squared plus 6X minus 40 equals 0 so now we're ready to factor and we want to find two factors of -40 that have a sum A+ 6 silver working with a negative product so that means we need one positive number and one negative number and because the song has a positive value the bigger about the number is going to be positive and smaller one so I'm going to start with 1 and 40 so the bigger numbers positive so the smaller number is -40 - 1 is 39 so that doesn't work then I'll move on to too and two + 2 - 20 is 18 so that doesn't work so then I'll move on to 3 but three doesn't divide evenly into 40 so we can skip it so then go on to 4 my hand turns a color 4 * 10 is 40 and 10-4 so it just happened that my pin change color to Pink and that's the pair that we're going to use so back to here factor that as x - 4 an x + 10 and those two factors equal 0 so one or the other of these have to equal 0 so we're going to set each factor equal to zero so for this if x -4 is the factor that is causing this expression to have a product of 0 then we'll solve that and will find it at seagulls positive for and then we'll solve the other factor x - I mean x + 10 people zero I will subtract 10 from both sides and get x equals negative 10 so our solution set is -10 and for several of you have asked me does it matter which order I write my answers in we usually write the smaller value first and then the larger so we write them from least to greatest another thing you'll notice is that if you replace the zero in the function here's the rub if you replace the zero with Y so y equals x squared plus at - 40 and you type this function into your graphing calculator you will find these Solutions the -10 and the 4 in the table and they are the zeros of the function so they will have a zero for a why this is a great way to check your work when you're finished factoring you will have to show that you are able to Factor according to the instructions but you can check your answers by looking in your graphing calculator to make sure that you did it correctly

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Lesson 5-3 Solve by Factoring - Trinomial

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