(x+4)(x-3)=-10

Question

why is there a negative ten there and what do i do with it

Answer 1

Yes you can FOIL it or solve the quadratic as shown.  OR, you can recognize that (x + 4)(x - 3 ) = -10 means that one binomial must be positive and the other negative, because the product of two unlike signs must be negative.  Then you can guess at values for x.  I got lucky and guessed at x = 1 which works as (4 + 1)(1-2) = (5)(-2) = -10.

 

For SAT math test you should keep methods like these in mind, as they save time, which at a premium in such tests.

Answer 2

Hi Isaiah,

 

First, you need to FOIL the expressions in the parentheses.

 

x² - 3x + 4x - 12 = -10

 

Then you add 10 to both sides to set your equation equal to zero . . .

while we're at it, we'll also combine like terms

 

x² + x - 2 = 0

 

Then, factor the polynomial (ask yourself, "what times what = -2?")

 

(x + 2)(x - 1)

 

Finally, set each factor equal to zero and solve for x

 

x + 2 = 0

      x = -2

 

x - 1 = 0

     x = 1

 

Just to be sure, substitute the values back in to check

 

(-2 + 4)(-2 - 3) = -10

(2) (-5) = -10

-10 = -10 . . . yep

 

(1 + 4)(1 - 3) = -10

(5) (-2) = -10

-10 = -10 . . . yep