Question 320559: help me solve equation (3x^2+49x+72) in form (3x+ ) (x+ )
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Looking at the expression  , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to  (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-27,-36,-54,-72,-108,-216
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*216 = 216
2*108 = 216
3*72 = 216
4*54 = 216
6*36 = 216
8*27 = 216
9*24 = 216
12*18 = 216
(-1)*(-216) = 216
(-2)*(-108) = 216
(-3)*(-72) = 216
(-4)*(-54) = 216
(-6)*(-36) = 216
(-8)*(-27) = 216
(-9)*(-24) = 216
(-12)*(-18) = 216
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | 216 | 1+216=217 | | 2 | 108 | 2+108=110 | | 3 | 72 | 3+72=75 | | 4 | 54 | 4+54=58 | | 6 | 36 | 6+36=42 | | 8 | 27 | 8+27=35 | | 9 | 24 | 9+24=33 | | 12 | 18 | 12+18=30 | | -1 | -216 | -1+(-216)=-217 | | -2 | -108 | -2+(-108)=-110 | | -3 | -72 | -3+(-72)=-75 | | -4 | -54 | -4+(-54)=-58 | | -6 | -36 | -6+(-36)=-42 | | -8 | -27 | -8+(-27)=-35 | | -9 | -24 | -9+(-24)=-33 | | -12 | -18 | -12+(-18)=-30 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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Answer:
So doesn't factor at all (over the rational numbers).
So is prime.
Make sure that you have the correct problem.
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