# How do you factor #x^2 - 22x + 120#?

##### 2 Answers

(x - 10)(x - 12)

#### Explanation:

Standard form

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)

Using reasoning:

#### Explanation:

Lets try and reason this out.

The coefficient of

The constant of 120 is positive So both of the ? are the same sign.

The

Note that

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: