Question 584928: 4xsquared+36x+35 i need two numbers that multiply to 56 but add to 36 (x+?)(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 :
1,2,4,5,7,10,14,20,28,35,70,140
-1,-2,-4,-5,-7,-10,-14,-20,-28,-35,-70,-140
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*140 = 140
2*70 = 140
4*35 = 140
5*28 = 140
7*20 = 140
10*14 = 140
(-1)*(-140) = 140
(-2)*(-70) = 140
(-4)*(-35) = 140
(-5)*(-28) = 140
(-7)*(-20) = 140
(-10)*(-14) = 140
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 | 140 | 1+140=141 | | 2 | 70 | 2+70=72 | | 4 | 35 | 4+35=39 | | 5 | 28 | 5+28=33 | | 7 | 20 | 7+20=27 | | 10 | 14 | 10+14=24 | | -1 | -140 | -1+(-140)=-141 | | -2 | -70 | -2+(-70)=-72 | | -4 | -35 | -4+(-35)=-39 | | -5 | -28 | -5+(-28)=-33 | | -7 | -20 | -7+(-20)=-27 | | -10 | -14 | -10+(-14)=-24 |
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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