SOLUTION: How do you Factor this equation? x squared+5x-14

Question 16570: How do you Factor this equation?
x squared+5x-14
Found 2 solutions by kikerkins, Earlsdon:
Answer by kikerkins(17) (Show Source): You can put this solution on YOUR website!
x squared+5x-14
Ax(sqaured)+BX+C
To factor your equation we must find factors of -14, that add or subtract to be 5. We have 1 and 14, No. 2 and 7, YES, 7-2 is 5.

(X+7)(X-2)
Because it is factors of -14, that means there is one positive and one negative factor( ie: +7,-2) and that makes sense because we need the 5 to stay positive, and 7-2 leaves us with a positive 5.
To check your work on any factoring problem, simply foil what you get [ (X+7)(X-2)], and it should equal the original quadratic(x squared+5x-14) if you did it correctly.

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
In factoring trinomials, such as you have, the idea is to get two binomials, which, when multiplied together, will give you back the trinomial you started with. Let's look at your trinomial expression (by the way, it's not an equation).

You would like to get two binomials of the form: (x + b)(x - c)
Look at the x^2 term of you trinomial. The only factors of x^2 are (x)(x) or (-x)(-x).
Now look at the last (constant) term (-14) of your trinomial. The factors of -14 are (-1)(14), (1)(-14), (-2)(7) or (2)(-7) Now, which combination of these would give you +5 when added together? Clearly, only (-2) + (7) = +5
Now we can try to put things together from the above analysis.
(x - 2)(x + 7) is a good possibility for the factors of
Check by multiplying the two factors using the FOIL method.
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