How would I solve the quadratic equation y=x^2-6x+8=0 by factoring?
Question:
Answer:
x^2-6x+8=0
1) Look at the first term, x^2. Look for two things with the product would be x^2. In this situation, you only have one option, which is x and x. So, you know you will have something like this (x...)(x...)
2) Look at the last term, +8. Look for two numbers with the product being +8. You will have (+8, +1), (-1, -8), (+2, +4), and (-4, -2). In this situation, (+8, +1), (-1, -8), (+4, +2), and (-2, -4) are the same as those terms listed above respectively.
3) Look at the middle term, -6x. You need to find a combination that will give you -6x.
a) The fact that the last term is positive and the middle term is negative show you that you need to pick two negative numbers. This will bring it down to two combinations, (-8, -1) and (-4, -2).
b) You need -6x. -8x -1x gives you -9x; so, (-4, -2) is the correct combination. And so (x-4)(x-2) is the correct combination.
(x-4)(x-2) = 0 which means that x can be 2 or 4
what two numbers can you multiply together to get 8, and if you add you get 6?
1 and 8
2 and 4
and that's it right?
notice that the 8 is positive, but the six is negative
that's because if you multiply two numbers having the same sign, the product will always have a positive number
however, if you add two numbers with the same sign, the sum will always have the same number
does 1 + 8 = 6?
no
does 2 + 4 = 6?
yes
so because the 6 is negative, you don't have +2 and +4, rather you have -2 and -4
so the answer is (x-2)(x-4)
simple (x-2)(x-4)
Points:- examples
+ve x +ve = +ve 3 x 5 = 15
+ve x -ve = -ve 3 x -5 = -15
-ve x -ve = +ve -3 x -5 = 15
addition
+ve + +ve = simply adding e.g 3+2 = 5
+ve + -ve = subtracting the smaller number frm biger number nd putting the sign of the bigger number..
e.g 8 + -2 = 6
-8 + 2 = -6
-ve + -ve = -ve
e.g -2 + -3 = -5
Note: -(-ve) = +ve
-(-8) = 8
Is very simple n u just need a bit of patience.
1. Find factors of 8- ie 2,2,2.
2. now use these 2s to make 6 by additin n multiplication- 2*2=4 so 4+2=6.
Now 6 is -ve so -4-2=-6
3.Now split the middle term.
x^2-4x-2x+8=0
x(x-4)-2(x-4)=0
(x-2)(x-4)=0
x=2,4
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