Solution - Simplification or other simple results

(x + 1) \cdot (2 x + 3)

(x+1)*(2x+3)

Step by Step Solution

Step 1 :

Equation at the end of step 1 :

  (2x² +  5x) +  3

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 2x²+5x+3

The first term is, 2x² its coefficient is 2 .
The middle term is, +5x its coefficient is 5 .
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 5 .

-6	+	-1	=	-7
-3	+	-2	=	-5
-2	+	-3	=	-5
-1	+	-6	=	-7
1	+	6	=	7
2	+	3	=	5	That's it

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

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (x+1)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x+1)
Step-5 : Add up the four terms of step 4 :
                    (2x+3)  •  (x+1)
             Which is the desired factorization

Final result :

  (x + 1) • (2x + 3)

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