Factor These: 2w^2-5w-10
Tuesday, September 7th, 2010Solution:
We can factor the expression 
as follows: 
To figure this out, we used the quadratic formula (see http://en.wikipedia.org/wiki/Quadratic_equation):
w = 
We recognized that y= 
is a quadratic equation in the form of y= 
where a=2, b=-5 and c=-10.
To confirm that our calculation are right, we decided to plot the graph of y = by plugging in various values of w.
As you can see, there is a root at approximately -1.3 and another root at approximately +3.8. So we know approximately what the values of a and b are. We could use a calculator to get closer and closer to the exact values of a and b. For example, if we try w=3.8, we get a value of y = -0.12. If we try a slightly different value, we can see if we’re getting closer to zero or farther away: w=3.81 produces a value of y=-0.018, so we know that 3.81 is a better approximation than 3.8. If we keep calculating closer approximations of the root, we will arrive at the value of b that we calculated using the quadratic formula: 
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