Question

Simplify:
a) (6x2 + 15x + 9) ÷ (2x + 3)​

Answer 1

Answer:

STEP1:Equation at the end of step 1 ((2•3x2) + 15x) - 9 STEP2:STEP3:Pulling out like terms

 3.1     Pull out like factors :

   6x2 + 15x - 9  =   3 • (2x2 + 5x - 3) 

Trying to factor by splitting the middle term

 3.2     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   =   -5     -3   +   2   =   -1     -2   +   3   =   1     -1   +   6   =   5   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

Final result :

3 • (2x - 1) • (x + 3)

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