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The trick to quadratic facotrization is to first check to see if there is a coefficient in front of x^2 that isn't 1. If that is the case you will need to consider two numbers that add to give you the cofficient in front of x and two numbers that multiply to give you a quantity equal to the coefficient in front of x^2 times the number without a variable x. In other words:
[tex]ax^2 + bx + c [/tex]
n+m = b
n*m = a*c
1) 10x^2+19x+6

a = 10 , b = 19 , c = 6 

Start by multiplying a * c = 10 * 6 = 60 

Now find two numbers that multiply to 60 and add up to 19...

We could use 15 and 4 because...

15 + 4 = 19
15 * 4 = 60

Now rewrite the expression...

10x^2 + 15x + 4x + 6

Now pull out common factors....

5x ( 2x + 3) + 2 ( 2x + 3 ) 

The factors of 10x^2+19x+6  are ( 5x + 2) ( 2x + 3)

2)  6x^2+11x+4  

a = 6 ,  b = 11 , c = 4 

Start by multiplying a * c = 6 * 4 = 24 

Now find two number that multiply to 24 and add up to 11

We could use 8 and 3 ...

8 + 3 = 11
8 * 3 = 24 

Now rewrite....

6x^2 + 8x + 3x + 4 

Pull out common factors...

2x ( 3x  + 4 ) + 1 ( 3x + 4) 

The factors of 6x^2+11x+4 are ( 2x + 1 ) ( 3x + 4 )

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