how ca we resolve into factor this: x2-9x+20

Question

resolve into factor: x2-9x+20

Answer 1

The fastest way is to just simply factor the first term and the last term. Since the first term is just x², it's pretty obvious that its factor is just x and x so you just need to test the 20. It will be either 2x10, -10x-2, 20x1, 4x5 etc. But your clue is choosing so is the middle term which is -9x. In this case, you just need to find factors that will add up to that and of course that will yield the same sign.

 

Example we choose 2 and 10. You will right the factors as (x+2)*(x+10). If you use FOIL method, you will get 12x as middle term, not -9x, meaning it's wrong. The answer is -4 and -5 because (x-4)*(x-5) will produce a middle term of -9x.

 

Another way is to just use the QUADRATIC FORMULA:

 

x = [-b±sqrt(b² - 4ac)]/2a; from the general form of ax² + bx + c = 0

 

The first factor is the one using the + in the ± and the second is using the -. It will yield x = 5 and x = 4. Then why not -5 and -4? Because those are not yet the factors, those are zeroes of the function. The binomial factor will show when you transpose the value on the other side giving you (x-5) = 0 and (x-4) = 0.

 

The third way is through COMPLETING THE SQUARES. This is basically the long method and how was the quadratic formula derived.