SOLUTION: I need help in factoring this equation! I also need it to be shown to me step by step because I dont know how to solve it! {{{ 2x^3-x^2-18x+9=0 }}}

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Question 293896: I need help in factoring this equation! I also need it to be shown to me step by step because I dont know how to solve it!
+2x%5E3-x%5E2-18x%2B9=0+
Found 2 solutions by jim_thompson5910, unlockmath:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+2x%5E3-x%5E2-18x%2B9=0+ Start with the given equation


+%282x%5E3-x%5E2%29%2B%28-18x%2B9%29=0+ Pair off the terms into two groups


+x%5E2%282x-1%29%2B%28-18x%2B9%29=0+ Factor out the GCF x%5E2 from the first group.


+x%5E2%282x-1%29-9%282x-1%29=0+ Factor out the GCF -9 from the second group. The goal is get a common term between the two groups.


+%28x%5E2-9%29%282x-1%29=0+ Factor out the GCF 2x-1 from the entire left side.


+%28x%2B3%29%28x-3%29%282x-1%29=0+ Factor x%5E2-9 to get %28x%2B3%29%28x-3%29 using the difference of squares formula.


I'll let you take it from here.

Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
Let's first off regroup this 2x^3-x^2-18x+9=0 to give us:
x^2(2x-1)-9(2x-1)=0 From this we have (2x-1) being multiplied by x^2 and -9 so we can use the distributive property to rewrite this as:
(x^2-9)(2x-1)=0 We can factor (x^2-9) to get the following:
(x-3)(x+3)(2x-1)=0 Are you with me so far?
Now we can solve for x to get:
x=3
x=-3
x=1/2
Of course, to check if these are correct, just plug them into the original equation.
Make sense?
RJ
Check out a book I wrote.
www.math-unlock.com