Factorise 2xsquared X 7x +3

 (-2x - 1) • (x + 3)

Step-by-step explanation:

3.2     Factoring  2x2 + 7x + 3

The first term is,  2x2  its coefficient is  2 .

The middle term is,  +7x  its coefficient is  7 .

The last term, "the constant", is  +3

Step-1 : Multiply the coefficient of the first term by the constant   2 • 3 = 6

Step-2 : Find two factors of  6  whose sum equals the coefficient of the middle term, which is   7 .

     -6    +    -1    =    -7

     -3    +    -2    =    -5

     -2    +    -3    =    -5

     -1    +    -6    =    -7

     1    +    6    =    7    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  6

                    2x2 + 1x + 6x + 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (2x+1)

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

                   3 • (2x+1)

Step-5 : Add up the four terms of step 4 :

                   (x+3)  •  (2x+1)

            Which is the desired factorization

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step-by-step explanation:

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