SOLUTION: please factor it!!!? 8x square + 5x - 200=0

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Question 887717: please factor it!!!?
8x square + 5x - 200=0
Found 2 solutions by jim_thompson5910, Alan3354:
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 :
1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800,1600
-1,-2,-4,-5,-8,-10,-16,-20,-25,-32,-40,-50,-64,-80,-100,-160,-200,-320,-400,-800,-1600


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to .
1*(-1600) = -1600
2*(-800) = -1600
4*(-400) = -1600
5*(-320) = -1600
8*(-200) = -1600
10*(-160) = -1600
16*(-100) = -1600
20*(-80) = -1600
25*(-64) = -1600
32*(-50) = -1600
40*(-40) = -1600
(-1)*(1600) = -1600
(-2)*(800) = -1600
(-4)*(400) = -1600
(-5)*(320) = -1600
(-8)*(200) = -1600
(-10)*(160) = -1600
(-16)*(100) = -1600
(-20)*(80) = -1600
(-25)*(64) = -1600
(-32)*(50) = -1600
(-40)*(40) = -1600

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :


First NumberSecond NumberSum
1-16001+(-1600)=-1599
2-8002+(-800)=-798
4-4004+(-400)=-396
5-3205+(-320)=-315
8-2008+(-200)=-192
10-16010+(-160)=-150
16-10016+(-100)=-84
20-8020+(-80)=-60
25-6425+(-64)=-39
32-5032+(-50)=-18
40-4040+(-40)=0
-11600-1+1600=1599
-2800-2+800=798
-4400-4+400=396
-5320-5+320=315
-8200-8+200=192
-10160-10+160=150
-16100-16+100=84
-2080-20+80=60
-2564-25+64=39
-3250-32+50=18
-4040-40+40=0



From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.


===============================================================



Answer:


So doesn't factor at all (over the rational numbers).


So is prime.


To solve you need to use the quadratic equation.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
It's an equation. Equations are solved.
Polynomials are factored.
----
please factor it!!!?
Is that a request, or a question? You have a ? on the end.
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