Question

X^2-22X+117
Factorise

Answer 1

Answer:

1.1     Factoring  x2-22x+117  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -22x  its coefficient is  -22 .

The last term, "the constant", is  +117  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 117 = 117  

Step-2 : Find two factors of  117  whose sum equals the coefficient of the middle term, which is   -22 .

     -117    +    -1    =    -118  

     -39    +    -3    =    -42  

     -13    +    -9    =    -22    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -13  and  -9  

                    x2 - 13x - 9x - 117

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

                   x • (x-13)

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

                   9 • (x-13)

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

                   (x-9)  •  (x-13)

            Which is the desired factorization

Final result :

 (x - 9) • (x - 13)

Step-by-step explanation:

Answer 2

${x}^{2} - 9x - 13x + 117 \\ = > x(x - 9) - 13(x - 9) \\ = >( x - 9)(x - 13) \\ = > x = 9 \: and \: 13$