Solve the following equation by factoring: 2x^2-5x-12=0
Answer choices:
A. x=-4 or x=-3/2
B. x=-4 or x=3/2
C. x=3/2 or x=4
D. x=-3/2 or x=4

D.x=-3/2 or x=4

Step-by-step explanation:

2x^2-5x-12=0

Factor

(2x  +b    ) (x+a       ) =0

We need to get -12  

Choices

-1 *12   -2 *6    -3*4  -4*3   -6*2   - 12*1

The first number is 2 because the x^2 coefficient is 2

2 * a +b = -5

Let a = -4  and b = 3

2*-4 +3 = -5

(2x +3)(x-4) =0

Using the zero product property

2x+3 =0       x-4 =0

2x =-3               x=4

x = -3/2

D. x=-3/2 or x=4

Step-by-step explanation:

To solve this, factor the equation 2x^2-5x-12. Since -12 is negative, one of the factors has to be negative and one has to be positive. Since the coefficient of x is -5, 1 times a factor plus 2 times another factor has to sum to -5. Trying factors, we realize that (2x+3)(x-4)=0 works. Solving, 2x+3=0 and x-4=0, or x=-3/2 or x=4.

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