Question

Factories 4x^2+28x+49

Answer 1

The first term is,  4x2  its coefficient is  4 .
The middle term is,  -28x  its coefficient is  -28 .
The last term, "the constant", is  +49 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 49 = 196 

Step-2 : Find two factors of  196  whose sum equals the coefficient of the middle term, which is   -28 .

     -196   +   -1   =   -197     -98   +   -2   =   -100     -49   +   -4   =   -53     -28   +   -7   =   -35     -14   +   -14   =   -28   That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  -14 
                     4x2 - 14x - 14x - 49

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (2x-7)
              Add up the last 2 terms, pulling out common factors :
                    7 • (2x-7)
Step-5 : Add up the four terms of step 4 :
                    (2x-7)  •  (2x-7)
             Which is the desired factorization

Answer 2

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