# Factoring Trinomials of the form ax2+bx+c with a =1.

## Presentation on theme: "Factoring Trinomials of the form ax2+bx+c with a =1."— Presentation transcript:

Factoring Trinomials of the form ax2+bx+c with a =1.
Dr. Marcia L. Tharp

How to factor a trinomial of the form ax2+bx+c when a=1
To factor a trinomial means to write it as a product of two binomials. For example x2+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. Adding the middle two terms you get X2+6x+8

To get this trinomial into its factored form we use F. O. I. L
To get this trinomial into its factored form we use F.O.I. L. in Reverse on x2+ 6x+8. Remember that the FIRST term x2 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 x2+ 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 x2+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 x2+ 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 x2+6x+8. Factors of 8 Sums of These Factors 1 and 8 1+8=9 2 and 4 2+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 x2+6x+8= (x+2) (x+4)

1) Factor x2 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.