SOLUTION: Help me find the real solutions of the equation by factoring: x to the 3rd power + 2x(square) - 16x - 32 = 0

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Question 470600: Help me find the real solutions of the equation by factoring:
x to the 3rd power + 2x(square) - 16x - 32 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, we must factor.




x%5E3%2B2x%5E2-16x-32 Start with the given expression


%28x%5E3%2B2x%5E2%29%2B%28-16x-32%29 Group like terms


x%5E2%28x%2B2%29-16%28x%2B2%29 Factor out the GCF x%5E2 out of the first group. Factor out the GCF -16 out of the second group


%28x%5E2-16%29%28x%2B2%29 Since we have the common term x%2B2, we can combine like terms



%28x%2B4%29%28x-4%29%28x%2B2%29 Now factor x%5E2-16 to get %28x%2B4%29%28x-4%29 (this a difference of squares)


So x%5E3%2B2x%5E2-16x-32 factors to %28x%2B4%29%28x-4%29%28x%2B2%29


In other words, x%5E3%2B2x%5E2-16x-32=%28x%2B4%29%28x-4%29%28x%2B2%29

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So this essentially means that x%5E3%2B2x%5E2-16x-32=0 becomes %28x%2B4%29%28x-4%29%28x%2B2%29=0


Now we move onto solving %28x%2B4%29%28x-4%29%28x%2B2%29=0



%28x%2B4%29%28x-4%29%28x%2B2%29=0 Start with the given equation.


x%2B4=0 or x-4=0, or x%2B2=0 Use the zero product property


x=-4 or x=4, or x=-2 Solve for 'x' in each equation.



So the three solutions are x=-4 or x=4, or x=-2