Question

M=-8r²+11r-6
T=-7r²-9r+14

Answer 1

Answer:

(3r+2)⋅(4−5r)

The first term is,  -15r2  its coefficient is  -15 .

The middle term is,  +2r  its coefficient is  2 .

The last term, "the constant", is  +8  

Step-1 : Multiply the coefficient of the first term by the constant   -15 • 8 = -120  

Step-2 : Find two factors of  -120  whose sum equals the coefficient of the middle term, which is   2 .

     -120    +    1    =    -119  

     -60    +    2    =    -58  

     -40    +    3    =    -37  

     -30    +    4    =    -26  

     -24    +    5    =    -19  

     -20    +    6    =    -14  

     -15    +    8    =    -7  

     -12    +    10    =    -2  

     -10    +    12    =    2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  12  

                    -15r2 - 10r + 12r + 8

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

                   -5r • (3r+2)

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

                   4 • (3r+2)

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

                   (-5r+4)  •  (3r+2)

            Which is the desired factorization

Step-by-step explanation:

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