How to factor this trinomial 5x^2+3x-14?

5x^2 + 3x - 14

First, set up
your two binomials.  Since the middle term is positive and the last term is negative,
you know one of the binomials contains addition and the other binomial contains
subtraction.

(___ + ___)(___ -
___)

The coefficient of the first term (5) is prime, so the
first terms in the binomials are 5x and x.

(5x + ___)(x -
___)

The last term (-14) can be factored a few
ways:

1, -14

14,
-1

2, -7

7,
-2

Now try out each combination.  Using FOIL, find the
combination that gives you the middle term 3x.

(5x + 1)(x -
14)     middle term = 69x    
no

(5x + 14)(x - 1)     middle
term = 9x     no

(5x + 2)(x -
7)     middle term = -33x    
no

(5x + 7)(x - 2)     middle
term = -3x

That last combination was close, except we need
the middle term to be postive 3x, not negative
3x.  So we switch the + and - signs and try again.

(5x -
7)(x + 2)     middle term = 3x

Use FOIL to
check.

5x^2 + 10x - 7x -
14

5x^2 + 3x - 14

Since this
was your original trinomial, it has been factored
correctly.

Solution:   (5x - 7)(x +
2)