Hi,

-x^2-7x+30

factoring

(-x + 3)(x + 10)

Checking the factoring using FOIL

F	First terms -x^2

O	Outside terms -10x

I	Inside terms    3x

L	Last terms     30

 

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
 





 
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to 30 and add to -7? Lets find out by listing all of the possible factors of 30

  

  

  Factors:

  

  1,2,3,5,6,10,15,30,

  

  -1,-2,-3,-5,-6,-10,-15,-30,List the negative factors as well. This will allow us to find all possible combinations

  

  These factors pair up to multiply to 30.

  

  1*30=30

  

  2*15=30

  

  3*10=30

  

  5*6=30

  

  (-1)*(-30)=30

  

  (-2)*(-15)=30

  

  (-3)*(-10)=30

  

  (-5)*(-6)=30

  

  note: remember two negative numbers multiplied together make a positive number

  

   Now which of these pairs add to -7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -7

  

  ||||||||
First Number
|
Second Number
|
Sum
1
|
30
|
1+30=31
2
|
15
|
2+15=17
3
|
10
|
3+10=13
5
|
6
|
5+6=11
-1
|
-30
|
-1+(-30)=-31
-2
|
-15
|
-2+(-15)=-17
-3
|
-10
|
-3+(-10)=-13
-5
|
-6
|
-5+(-6)=-11
  
  None of these factors add to -7. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.
 

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