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math question factoring

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2 Answers

4X^2 +14X + 6
 
Let 's factor 2 first:
 
2 ( 2X^2 +7X + 3)
 
 To factor 2X^2 + 7X + 3      /  2 numbers, whose Sum is 7 . and product is 2*3 = 6, are( 6 ,1)
 
2 ( 2X^2 + 6X + X + 3 )     / break 7x= 6X +X
 
2 ( 2X^2 +6X + X + 3 ) =
 
2 [ 2X ( X + 3 ) + ( X +3) ] =
 
2 ( X+3) ( 2X + 1)     
Factor 4x2+14x+6
 
The factors will be either (4x+m)(x+n) or (2x+m)(2x+n)
 
(4x+m)(x+n) = 4x2 + (4n+m)x + mn, so (4m+n)=14, mn=6
 
or
 
(2x+m)(2x+n) = 4x2 + (2m+2n) + mn, so (2m+2n)=14, mn=6
 
Start by looking at the factors of m*n = 6: 6*1, 3*2, 2*3, 1*6.  Let's look at the first potential factors, (4x+m)(x+n).  If we pick m=2 and n=3, then
 
4x2 + (4*3+2)x + (3*2) = 4x2 + 14x + 6  which works!
 
So our factors are:
 
(4x+2)(x+3)

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