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10n^3-25n^2-16n+40 I'm so lost on this please help

User Mcestone
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1 Answer

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I think you're factoring this...? You can do that by grouping here. Put the 4 terms in groups of 2 and factor out the greatest common factor. What's left behind is a common binomial factor that can also then be factored out. Like this:

(10 n^(3) -25 n^(2))-(16n+40)
Factoring what we can out of both sets gives us this:

5 n^(2) (2n-5)-8(2n-5)
The 2n-5 is a common factor between both the sets of terms, which in turn can also be factored out:

(2n-5)(5 n^(2)-8)
I'm not exactly sure what you are doing with this, but we can keep factoring for the sake of completeness. The 5 n-squared term can also be factored:

5 n^(2)-8=0 and
5 n^(2) =8 and
n^(2) = (8)/(5) so
n= ( √(8) )/( √(5) ). Simplifying that down its simplest is this:

n=+/- (2 √(10) )/(5)
So your three factors for that polynomial are

(n- (5)/(2) ),(n- (2 √(10) )/(5) ),(n+ (2 √(10) )/(5) ),

User Abhilash Ranjan
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