Question

x^ 2 + 27x - 182 :- factorize

Answer 1

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Step  1  :Trying to factor by splitting the middle term 
 1.1     Factoring  x2+27x-182 
The first term is,  x2  its coefficient is  1 .
The middle term is,  +27x  its coefficient is  27 .The last term, "the constant", is 
 -182 
Step-1 : Multiply the coefficient of the first term by the constant   1 • -182 = -182 
Step-2 : Find two factors of  -182  whose sum equals the coefficient of the middle term, which is   27 .
      -182    +    1  =    -181
      -91+    2    =    -89    
  -26    +    7    =    -19  
    -14    +    13    =    -1  
    -13    +    14    =    1      
-7    +    26    =    19
      -2    +    91    =    89  
    -1    +    182    =    181
Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored
Final result :  x2 + 27x - 182
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Hope my answer helped … ☺

Answer 2

actually the question should be x^2 +27x + 182

so, x^2 +27x + 182 = x^2 + 13x +14x +182 = x(x+13) + 14(x+13) = (x+13) (x+14)

Thus, the factors are (x+13) and (x+14)

Hope this helps you...