SOLUTION: factor.write prime if the expression cannot be factored : S exponent2 -S-6

Algebra ->  Expressions -> SOLUTION: factor.write prime if the expression cannot be factored : S exponent2 -S-6       Log On


   

Question 605546: factor.write prime if the expression cannot be factored : S exponent2 -S-6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression s%5E2-s-6, we can see that the first coefficient is 1, the second coefficient is -1, and the last term is -6.


Now multiply the first coefficient 1 by the last term -6 to get %281%29%28-6%29=-6.


Now the question is: what two whole numbers multiply to -6 (the previous product) and add to the second coefficient -1?


To find these two numbers, we need to list all of the factors of -6 (the previous product).


Factors of -6:
1,2,3,6
-1,-2,-3,-6


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


These factors pair up and multiply to -6.
1*(-6) = -6
2*(-3) = -6
(-1)*(6) = -6
(-2)*(3) = -6

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -1:


First NumberSecond NumberSum
1-61+(-6)=-5
2-32+(-3)=-1
-16-1+6=5
-23-2+3=1



From the table, we can see that the two numbers 2 and -3 add to -1 (the middle coefficient).


So the two numbers 2 and -3 both multiply to -6 and add to -1


Now replace the middle term -1s with 2s-3s. Remember, 2 and -3 add to -1. So this shows us that 2s-3s=-1s.


s%5E2%2Bhighlight%282s-3s%29-6 Replace the second term -1s with 2s-3s.


%28s%5E2%2B2s%29%2B%28-3s-6%29 Group the terms into two pairs.


s%28s%2B2%29%2B%28-3s-6%29 Factor out the GCF s from the first group.


s%28s%2B2%29-3%28s%2B2%29 Factor out 3 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.


%28s-3%29%28s%2B2%29 Combine like terms. Or factor out the common term s%2B2


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


Answer:


So s%5E2-s-6 factors to %28s-3%29%28s%2B2%29.


In other words, s%5E2-s-6=%28s-3%29%28s%2B2%29.


Note: you can check the answer by expanding %28s-3%29%28s%2B2%29 to get s%5E2-s-6 or by graphing the original expression and the answer (the two graphs should be identical).
--------------------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
--------------------------------------------------------------------------------------------------------------