Factoring trinominals

Question

a factor of 24 that give you a sum of negative four

 

Answer 1

Let x and y be the factors. You have a system of two equations

                                  xy = 24  and x+y = -4

from the second equation y = -(x+4). Substitute y in the first equation by -(x+4). You will obtain

                     -x(x+4) = 24    or x(x+4) = -24     or x^2 +4x +24 + 0

Then follow the steps shown by John R.

Answer 2

I assume you are factoring the trinomial:

x² - 4x + 24

The trinomial cannot be factored, but we can find the values of x that make the trinomial equal 0 by completing the square.

x² - 4x + 24 = 0                        Set the trinomial equal to 0

x² - 4x = -24                            Subtract 24 from each side

x² - 4x + 4 = -24 + 4                Add 4 to each side ([-4/2]² = + 4)

x² - 4x + 4 = -20                      Simplify the right side of the equation

(x - 2)² = -20                           Factor the left side of the equation

x - 2 = +/- √(-20)                    Take the square root of each side

x - 2 = +/-2i√5                        Simplify the right side

x = 2 +/- 2i√5                         Add 2 to each side

The "factors" of 24 that give a sum of negative four would be -2 + 2i√5 and -2 - 2i√5.