SOLUTION: Factor completely: x2 � 5x � 14 Factor completely: 3x2 � 2x � 8 Factor completely: 24x2 + 10x � 4

Question 27450: Factor completely:
x2 � 5x � 14

Factor completely:
3x2 � 2x � 8

Factor completely:
24x2 + 10x � 4

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Hint: You can indicate x-squared by using the "caret", thus: x^2
Factor completely:
1)
If this trinomial expression factors, the factors will take the form: (x+m)(x+n) where: (m)*(n) = -14 and (m)+(n) = -5
Try m = -7 and n = +2
(2)(-7) = -14 and (2) + (-7) = -5
The factors are: (x-7)(x+2) Check using the FOIL method:
=
2)
If this trinomial expression factors, the factors will take the form: (3x+m)(x+n) where: (m)*(n) = -8 and (m)+(3n) = -2
Try m = 4 and n = -2
(4)*(-2) = -8 and (4)+3(-2) = 4-6 = -2
The factors are: (3x+4)(x-2) Check using the FOIL method:
=
3)
This one requires a little more work because of the lager number of possible factors of the coefficient of x^2 (24).
First, list the factor-pairs of 24:
1 X 24 = 24
2 X 12 = 24
3 X 8 = 24
4 X 6 = 24
The choices of factors of the constant term in the given expression are:
1 X -4 = -4
-1 X 4 = -4
2 X -2 = -4
Now you need to select a pair from the first list of factors and a pair from the second list of factors and, through an educated trial-and-error process, combine them to form the factors of the given expression.
I would try 3 and 8 from the first list and 2 and -2 from the second list. Let's see what happens:
= Ok, a lucky(?) guess.

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