x^2 + 3x -10=0

Question

solve solution by factoring 

Answer 1

First, consider F-O-I-L (First-Outside-Inside-Last):

 

    (x+a)(x+b) = x² + bx + ax + ab = x² + (a+b)x + ab

 

Now, if the coefficient of x² is not 1, then the first step is to divide by that coefficient.  That gives:

    x² + 3x + (-10) = 0

 

   So, (a+b) = 3

         a*b = -10

 

    Since a*b is negative, either a or b must be negative, but not both.

 

    The sum a+b is 3.

 

    The factors of 10 are 1, 2, 5, and 10.  Combining (-2) with (5), we get a sum of (3) and a product of (-10).  So, pick either, a=-2 and b=5:

    x² + 3x -10 = 0

    (x-2)(x+5) = 0             [The Multiplicative Property of Zero says that x=3 or x=-5 or both.]

Answer 2

Hi John,

 

x^2 + 3x -10=0

(x - 2)(x + 5) = 0

x = 2 or x = -5

the solution set is x={-5, 2}