Question 586045: Can you please help me factorise these three questions?
a) 10x^2 - x -3
I have tried the grouping and cross and method but come up blank. Also there are no common factors.
b) 5y^3 - 5000
It may be the difference of two cubes but 5000 does not have a cubed root...?
c) convert 0.346 to a fraction where the 4 and 6 in 0.346 are recurring
I have completed the same question for 0.04 where the four is recurring but the method I used (let x = 0.0444444....; 100x = 4.44444....; 99x=4.4: therefore x = 44/990)does not work for 0.346.
Thankyou very much for your help!!!!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first one to get you stared.
a)
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 :
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-30) = -30
2*(-15) = -30
3*(-10) = -30
5*(-6) = -30
(-1)*(30) = -30
(-2)*(15) = -30
(-3)*(10) = -30
(-5)*(6) = -30
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 | -30 | 1+(-30)=-29 | | 2 | -15 | 2+(-15)=-13 | | 3 | -10 | 3+(-10)=-7 | | 5 | -6 | 5+(-6)=-1 | | -1 | 30 | -1+30=29 | | -2 | 15 | -2+15=13 | | -3 | 10 | -3+10=7 | | -5 | 6 | -5+6=1 |
From the table, we can see that the two numbers  and  add to (the middle coefficient).
So the two numbers and both multiply to and add to
Now replace the middle term  with  . Remember, and add to . So this shows us that  .
 Replace the second term with .
 Group the terms into two pairs.
 Factor out the GCF  from the first group.
 Factor out  from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.
 Combine like terms. Or factor out the common term 
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Answer:
So factors to .
In other words,  .
Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
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Jim
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