Question 277983: factor trinomials 4x^2+9x+10=
Found 2 solutions by Edwin McCravy, richwmiller:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
Multiply the 4 by the 10, getting 40
Write down all the products of two integers which gives +40
40*1
20*2
10*4
8*5
Now out beside all those write their sum,
since +40 is positive. (If it had been negative
we would have found their difference)
40*1 40-1 = 39
20*2 20-2 = 18
10*4 10-4 = 6
8*5 8-5 = 3
Notice that the coefficient of the middle term, 9,
in absolute value, does not appear in the column of
differences above. Therefore the trinomial does not factor.
Edwin
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website!
| Solved by pluggable solver: Factoring using the AC method (Factor by Grouping) |
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 :
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*40 = 40
2*20 = 40
4*10 = 40
5*8 = 40
(-1)*(-40) = 40
(-2)*(-20) = 40
(-4)*(-10) = 40
(-5)*(-8) = 40
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 | 40 | 1+40=41 | | 2 | 20 | 2+20=22 | | 4 | 10 | 4+10=14 | | 5 | 8 | 5+8=13 | | -1 | -40 | -1+(-40)=-41 | | -2 | -20 | -2+(-20)=-22 | | -4 | -10 | -4+(-10)=-14 | | -5 | -8 | -5+(-8)=-13 |
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.
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