Question

factorise -18+11x-x2​

Answer 1

Answer:

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Step-by-step explanation:

-18+11x-x^2  

Step by Step Solution  

  -x2 + 11x - 18  =   -1 • (x2 - 11x + 18)  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -11x  its coefficient is  -11 .

The last term, "the constant", is  +18  

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

Step-2 : Find two factors of  18  whose sum equals the coefficient of the middle term, which is   -11 .

     -18    +    -1    =    -19  

     -9    +    -2    =    -11    That's it

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

                    x2 - 9x - 2x - 18

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

                   x • (x-9)

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

                   2 • (x-9)

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

                   (x-2)  •  (x-9)

            Which is the desired factorization