Question

Factorise the given question: 3p^-7p-6​

Answer 1

Answer:

(p−3)⋅(3p+2)

Step-by-step explanation:

STEP 1 :

Equation at the end of step 1

(3p2 -  7p) -  6

STEP 2 :

Trying to factor by splitting the middle term

2.1     Factoring  3p2-7p-6  

The first term is,  3p2  its coefficient is  3 .

The middle term is,  -7p  its coefficient is  -7 .

The last term, "the constant", is  -6  

Step-1 : Multiply the coefficient of the first term by the constant   3 • -6 = -18  

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -7 .

-18 + 1  = -17  

-9 +2 = -7 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  2  

                    3p2 - 9p + 2p - 6

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

                   3p • (p-3)

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

                   2 • (p-3)

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

                   (3p+2)  •  (p-3)

            Which is the desired factorization

Final result :

 (p - 3) • (3p + 2)