Can Someone show me an example about Factoring Trinomials: x^2 + bx + c?

x^2+2*x*1/2b+(1/2b)^2


-(1/2b)^2+c


=(x+1/2b)^2-[(b^2-2c)/2]


=[x+1/2b+rt{b^2-2c/2}]


[x+1/2b-rt{b^2-2c)/2}]

Can Someone show me an example about Factoring Trinomials: x^2 + bx + c?
x^2 +bx + c


First, you start out with (x+ )(x+ ) or (x- )(x- )


The reason you start this way is when you multiply two positive numbers or two negitive numbers, you will get a positive number.





Now, you have to figure out what the multiples of c are where if added together they will equal b.





A better example.





t^2 + 5t - 24


(t- )(t+ ) We use one negitive and one positive since that is the only way we will get -24 when the numbers are multiplied together.





Now, create a list of factors for 24: 1x 24, 2 x 12, 3 x 8, 4 x 6





Now, which one when added together will equal 5?


24-1=23


12-2=10


8-3=5, that is it.





So, (t-3)(t+8)
Reply:assuming it is x^2 + bx + c (and not ax^2 + bx + c), you can use the FOIL (First, Outside, Inside, Last) method.





ex. factoring x^2 - 5x - 6 = (x + 2) (x - 3)





= x * (-3) + x*x + 2*x - 2*3





see the source below for a better explanation.
Reply:ax^2+bx+c





So long as the coeffecient of x^2 is 1, then you just need to find two numbers that when multiplied together equal c, and when added together equal b.





ex. x^2+8x+12


6(2)=12


6+2=8


so the correct answer is (x+6)(x+2)





However, if the coeffecient of x^2 , which I'll call d, isn't 1 then you have more to think about. You need to find two numbers that when multiplied together equal a. When, one of these two numbers is multiplied with one of the factors of c and added to the other factor of d multiplied by the other factor of c, it should equal b. The factor of a cannot be in the same set of parentheses as the factor of c you multiplied it by in the earlier step. I'll give an example to help you understand better.





ex. 6x^2-7x-5


1(-5)=-5 Both 1 and -5 are factors of c


3(2)=6 Both 3 and 2 are factors of a


3(1)=3 One factor of a multiplied by one factor of c


2(-5)=-10 The other factor of a multiplied by the other factor of c


3+-10=-7 Add the answers to the last two steps together and


you get b


So the correct answer is:


(3x-5)(2x+1)


NOTE: 3 is not in the same set of parentheses as 1, and 2 is not in the set of parentheses as -5.





When you FOIL your factored answer, you get back your original problem, if you factored it correctly.