math question factoring

Question

4x^2+14x+6

Answer 1

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)     

Answer 2

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)