Question

how do you factor trinomials

Answer 1

easiest is the type

x^2 + bx + c

best way is by examples

x^2 + 5x + 6
factors are of the form
(x + a)(x + b)

ab must equal + 6 and a + b must = + 5
a and b are 2 and 3.
so we get
x^2 + 5x + 6 = (x + 2)(x + 3)

x^2 - x - 6:

ab = -6 and a + b = -1
so a = -3 and b = +2
x^2 - x - 6 = (x - 3)(x + 2)

x^2 - 12x + 35
ab = + 35 and a + b = -12

a = -5 and b = -7
x^2 - 12x + 35 = ( x - 5)(x - 7)

Answer 2

To factor trinomials you have to first start off by knowing what the numbers will be. So if you have an equation that has x^2+6x+5 ( which is a pretty easy one ), you would have to know that the x will get distributed two times, the 6 will have to be added up with the same numbers as used to multiply to get 5. I know that this is pretty confusing to understand, but you will get to know more about it when we will solve the problem.

What I meant by distributing the x two times is that there will be two parentheses settled up. And you must do that before even starting the equation. The reason for why there will be two x is precisely understood because there is the x being squared. Now this time, you have to start off with the 5 at the end. A similar formula to that equation is (x+/-a)(x+/-b). I understand that this is quite confusing. What I meant is that there needs to be two factors and these two factors will have to multiply to 5. The tricky part is that these two factors (positive or negative) will need to be added to get 6. So what are the factors of 5? The only factors are 1 and 5, so 5 is a prime number. Since the 5 is a prime number and only 1x5=5, we need to know if the 1 and the 5 can add up to positive 6. Always remember that the plus or minus sign are two notifiers whether the number will be positive or negative if only the sign is in front of the number. Also the x of the 6, or any number, doesn't count towards the solving. So if we add 1+5 it will equal to 6. Now we got our two numbers, 1 and 5.

To fill in the blanks of (x+/-___)(x+/-____), we will need our two numbers, 1 and 5. Since these two numbers are positive, there will be a plus sign, not a minus. The completed equation will be (x+1)(x+5).