Factor the expression 4x^2 - 12x - 7

(2x+1) (2x-7)

Step-by-step explanation:

Multiply the coefficient of the first term by the constant   4 • -7 = -28

Find two factors of  -28  whose sum equals the coefficient of the middle term, which is   -12

(  -28    +    1    =    -27  

     -14    +    2    =    -12  )

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  2  

                    4x2 - 14x + 2x - 7

Add up the first 2 terms, pulling out like factors :

                   2x • (2x-7)

             Add up the last 2 terms, pulling out common factors :

                    1 • (2x-7)

Add up the four terms :

                   (2x+1)  •  (2x-7)

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