Check out this simple Math trick

Example (1)Divide X3+6x2+11x+6= by x+3 just let x+3=0 so x=−3 multiply by −1= 3 and divide by x so it make +3/x use it to multiply x3 it will give you +3x2 that means +3x2 must appear in the next to X3 if +3x2 appear the remaining will be +3x2 then you multiply the remaining +3x2 multiply by +3/x again will give +9x if +9x is appers next to 3x2 then the remaining is 2x so you form a new equation like this x3+3x2+3x2+9x+2x+6 then you factorize x2(x+3)+3x(x+3)+2(x+3)=(x+3)(x2+3x+2) so X3+6x2+11x+6=0 by x+3 divide by x+3=x2+3x+2
Example (2) divide 2x3−x2−25x−12= by 2x+1 so just let 2x+1=0 and 2x=−1and x=−1/2 multiply by −1 and divide by x so it form 1/2x so multiply the first term by 1/2x= +x2 so +x2 must be in the next term and if x2 is in the next tern the remaining will be −2x2 then multiply the remaining that is−2x2 by 1/2x it will give –x so this must be in the next term and then it will remain −24x so you rewrite the equation like this
2x3 + x2 − 2x2 – x −24x−12 so you factorize it becomes x2(2x+1) –x(2x+1)−12(2x+1)=(2x+1)(x2−x−12) so 2x3−x2−25x−12 divide by 2x+1 = x2−x−12

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