factoring a polynomial: v^2 - 22v - 75

G

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Please help-
factor each polynomial completely:

. . .v^2 - 22v - 75

thanks-caron
 

stapel

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Feb 4, 2004
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Hint: Find factors of 75 that are 22 units apart.

Eliz.
 

jonboy

Full Member
Joined
Jun 8, 2006
Messages
547
Hello Caron!

Factor: \(\displaystyle \L v^2\, -\, 22v\, -\, 75\)
Ok since we have \(\displaystyle v^2\) in our polynomial we need to think: What are two numbers that multiply to give us -75 and add up to -22? So after playing w/this a little bit you arrive at -25 and 3. Notice: 25 * -3 = -75 and -25 + (3) = -22. If we could not find these two number then we could just use the Quadratic Formula since I doubt you have learned difference of squares. Ok?


So since 3 > -25 our answer is:


\(\displaystyle \;\;\;\L (v+3) (v-25)\)


Check by FOIL:


\(\displaystyle \L \;\;\;v^2-25v+3v-75\,\to\,v^2\,-\,22v\,-\,75\)


Hope this helps. :D
 
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