Presentation on theme: "Factoring Trinomials of the form ax 2 +bx+c with a =1. Dr. Marcia L. Tharp."— Presentation transcript:
Factoring Trinomials of the form ax 2 +bx+c with a =1. Dr. Marcia L. Tharp
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
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
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.
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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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.
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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