Question

Factor.

x^2-5x+6
A. (x+2)(x+3)
B. (x-5)(x-1)
C. (x-2)(x-3)
D. (x-6)(x+1)

Answer 1

C

Explanation:

`{x}^(2) - 5x + 6`

First, let's solve this quadratic equation:

`{x}^(2) - 5x + 6 = 0`

a = 1, b = -5, c = 6

`d = {b}^(2) - 4ac = ( { - 5})^(2) - 4 * 1 * 6 = 25 - 24 = 1 > 0`

`x1 = ( - b - √(d) )/(2a) = (5 - 1)/(2 * 1) = (4)/(2) = 2`

`x2 = ( - b + √(d) )/(2a) = (5 + 1)/(2 * 1) = (6)/(2) = 3`

Now, in order to factorize the equation, we have to write it in the following form:

`(x - x1)(x - x2)`

`(x - 2)(x - 3)`