Question

Factorise x power 2 + 25 x - 54 ​

Answer 1

Answer:

1.1     Factoring  x2-25x-54 

The first term is,  x2  its coefficient is  1 .

The middle term is,  -25x  its coefficient is  -25 .

The last term, "the constant", is  -54 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -54 = -54 

Step-2 : Find two factors of  -54  whose sum equals the coefficient of the middle term, which is   -25 .

     -54   +   1   =   -53     -27   +   2   =   -25   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -27  and  2 

                     x2 - 27x + 2x - 54

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

                    x • (x-27)

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

                    2 • (x-27)

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

                    (x+2)  •  (x-27)

             Which is the desired factorization

Step-by-step explanation:

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