Trinomial+Where+A=1

Trinomial where a=1 In order to simplify a trinomial when a is 1 you must reverse FOIL. When you reverse FOIL you will end up with two binomials being multiplied together. Because a is 1, you know that every time you have this type of problem the first value in each binomial will be x.

 x²+5x+6

In this case, when you reverse FOIL you will end up with a binomial that looks something like this: (x + _)(x+ _) The addition signs are plugged into the new binomials from the original.Because the blue circle has a positive that means each sign has to be the same, either two positives or negatives. Because the red circle also has a positive, the signs need to be positive.From this point on you now need to find your unknown values. To find this, you need numbers that will multiply to give you 6, and add up to give you 5. Your solution should be: **(x + 2) (x + 3) **

 x²-5x+6

In this case, you again have the** blue ** circle with a positive, so again the sign in the two binomials must be the same. And because there is a negative in the ** red **, the signs must be negative. We know that our equation will start out as: **(x -_) (x -_) ** Now we need to find two negatives that multiply together to equal positive 6 and add up to equal negative 5. Your solution should be: **<span style="color: #2d176e; display: block; font-family: Helvetica,sans-serif; font-size: 130%; text-align: center;">(x - 2) (x - 3) **

<span style="display: block; font-family: helvetica,sans-serif; font-size: 24px; text-align: center;"> x²-2x-15 <span class="st" style="font-family: Helvetica,sans-serif; font-size: 170%;"> In this case we have two negative signs. Because the ** blue ** circle includes a negative sign, the signs in the binomial must be opposites. Now it is harder than just plugging numbers in, you must place them correctly with the sign. Because the ** red ** circle contains a negative sign, when you plug in values for the unknown, you must place the larger of the two numbers with the negative sign. So far we have: (x + _) (x - _) We now need to fill in the blanks with two numbers that multiply to equal negative 15 and add up to equal negative 2. The solution should read: __**(x + 3) (x - 5)**__ *Five is bigger than three, therefore when you add up -5 + 3 it will equal the negative 2 and also multiply for negative 15.

<span style="display: block; font-family: helvetica,sans-serif; font-size: 140%; text-align: center;">x²+2x-15

<span style="display: block; font-family: helvetica,sans-serif; font-size: 110%; text-align: center;">We have two different signs again in this case, and the blue circle has a negative, which means in our binomial the signs must be different. This time, because the red circle has a positive sign, the larger number of the two must be positive. We should have this: (x + _) (x - _) We now need a pair of numbers that add to positive 2 and multiply to negative 15. Our solution should be: __** (x + 5) (x - 3) **__ *Five is bigger than three, therefore when you add up 5 + -3 it will equal the negative 2 and also multiply for negative 15. = =