Are there any quick ways to find two numbers that can both be multiplied and added to reach certain numbers? For example: If I wanted to find a number that multiplied to 14 and added to 9, I would use 7 and 2 because 7*2=14 and 7+2=9. You use this a lot when factoring by grouping, and I was wondering if there were any tips to finding the two numbers faster, especially when dealing with larger numbers that have more factors.
No matter how big the number is, you should be able to list its factors: For example, if the number is 36, then its factors are 9 x 4, 6 x 6, 12 x 3. So either the 9 & 4 or 6 & 6 or 12 & 3 will go into each of your parenthesis when grouping. Before trying them look to see what the value of your X is in the middle of the equation and which of those two numbers when added or subtracted will give you the final result.
Example: x^2 + 9x -36. By seeing the 36 at the end, we know we must use a set of the factors listed above. But which set from above will give you +9x in the middle, it must be a +12 and a -3. Hope this helps :)