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Factoring Trinomials of the form ax 2 +bx+c with a =1. Dr. Marcia L. Tharp

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How to factor a trinomial of the form ax 2 +bx+c when a=1 To factor a trinomial means to write it as a product of two binomials. For example x 2 +6x+8= (x+2) (x+4) two binomials Remember we can use F.O.I. L. to multiply out (x+2) (x+4) we get: ctoring trinomials is an important Algebraic skill. It is used in higher-level mathematics and science. Besides that you will need it to simplify some polynomial expressions and solve more complex equations. X 2 +6x+8 Adding the middle two terms you get

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To get this trinomial into its factored form we use F.O.I. L. in Reverse on x 2 + 6x+8. Remember that the FIRST term x 2 came from its factors x (x). So these two factors become the first terms in each binomial. Remember that the LAST term in each binomial came from factors of the LAST term 8 in x 2 + 6x+8 So 8 breaks down to 1(8) or 2(4). We need to choose which pair of factors 1 and 8 or 2 and 4 we want to become the last terms in each binomial

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To do this we look at the middle terms of x 2 +2x+4x+8. When we use F.O. I. L. to multiply the OUTSIDE and INSIDE terms in (X+2) (x+4) The inside and outside products are 2x and 4x. Their sum is 6x. So we are looking for factors of 8 (the constant term) that add to 6 to get the coefficient of the middle term in x 2 + 6x+8.

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Lets make a table to organize what we know. We use a table to find two factors of 8 who sum to 6 the coefficient of the middle term in x 2 +6x+8. Factors of 8Sums of These Factors 1 and 81+8=9 2 and 42+4=6 So 2 and 4 have a sum of 6 and a product of 8. So these are the factors of 8 we use as the last terms of the binomial (x+__)(x+__). Therefore x 2 +6x+8= (x+2) (x+4)

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Interactive FOIL Exploration Print this page. First get the Live Math Plug in at: Be sure to download the plug in for your browser Internet Explorer or Netscape. Next click on the link to the Live Math Exploration and follow the directions in it. Finally click the back button on your browser to come back to this lesson. If for some reason this page does not work click back until you get to this presentation ignore the link and click past this page.

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Review To Factor A Trinomial ax 2 +bx+c when a=1 Print this page. 1) Factor x 2 into x (x). 2) Find two numbers who are factors of the last term (constant term), c, and whose sum equals the coefficient of the middle term (x-term) b. 3) Use the two numbers found in the above step, including their signs, to write the trinomial in factored form. The trinomial in factored form will be: (X + a number) (X + a number) Now go on to the practice problems.

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Practice Problems Try this practice. Factor each trinomial below. 1) x 2 +7x+12 answeranswer 2) x 2 -6x+8 answeranswer 3) x 2 -18x+80 answeranswer 4) x 2 -2x-80 answeranswer 5) b 2 -11b+18 answeranswer 6) x 2 +8xy+15y 2 answeranswer

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Now click on the door to go on to How to factor the form ax 2 +bx+c with a>1

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