Trinomial+Where+a+Equals+1

Trinomial Where A = 1

Trinomials where a=1 (also known as reverse FOIL)

There are two different types of factoring by reverse FOIL, the first one being where "c" is positive, and the other one where "c" is negative. We'll do the first one first, because that makes sense.

The standard form of one of these trinomials is x 2 +bx+c. Think about where the 'b' and 'c' terms come from. 'C' is the product of the two numbers in the binomials, while 'b' is the sum. You also have to think about the sign you put in each of the binomials. If 'c' is positive, the two signs are the same, so you have to look at the sign in front of the middle term to determine if you should put a plus sign or a minus sign.

For example, factor: x 2 +3x+2 Since it's just x 2 you put an x at the beginning of each binomial. (x )(x ) You can see that 3x is positive, so you put a plus sign in the binomials. (x+ )(x+ ) Now think about two numbers whose product is 2 and whose sum is 3. 1 and 2 work, so you complete the binomials with them. (x+1)(x+2)

The other type is where 'c' is negative. It's very similar to the first type, but instead of being the sum of the two numbers, the middle term is the difference of the two numbers. The sign in front of the middle term shows if the larger of the two numbers is positive or negative.

For example, factor x 2 -5x-14 Put an x in each binomial. (x )(x ) Put a plus sign in one, and a minus in the other. (x+ )(x- ) Now think about two numbers whose product is 14 and whose difference is 5. 7 and 2 work, so now all you have to figure out is which one is positive and which is negative. Since 7 is larger than 2, and the middle term is negative, 7 will be the negative and 2 will be the positive. (x+2)(x-7)

Here is a great game to get some practice in a fun way.