How do you factor #x^2 - 22x + 120#?
(x - 10)(x - 12)
Use the new Transforming Method (Google, Yahoo)
Find 2 numbers knowing sum (- 22 = b) and product (ac = 120). The numbers have same sign because ac > 0.
Factor pairs of (120) --> ...(6, 20)(10, 12). This last sum is 22 = -b. Then the opposite sum (-10, -12) gives the 2 numbers: -10 and -12 (sum = b)
y = (x - 10)(x - 12)
Lets try and reason this out.
The coefficient of
The constant of 120 is positive So both of the ? are the same sign.
Stating the obvious, the constant of 120 ends in zero so it has to be the product of two numbers where one of them ends in either 5 or 0.
As the square root is close to 11 lets consider the possibility one of the factors as being 10.
So we have: