# How do you factor completely #-6m^5+34m^3-40m#?

#= -2m(sqrt(3)m-sqrt(5))(sqrt(3)m+sqrt(5))(m-2)(m+2)#

We can use an AC method to find quadratic factors:

Putting it all together:

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To factor completely the expression ( -6m^5 + 34m^3 - 40m ), first, we can factor out the greatest common factor, which is 2m:

[ 2m(-3m^4 + 17m^2 - 20) ]

Now, we focus on factoring the quadratic expression inside the parentheses, ( -3m^4 + 17m^2 - 20 ). This can be factored as:

[ -3m^4 + 17m^2 - 20 = -(3m^2 - 5)(m^2 - 4) ]

Further, we can factor ( 3m^2 - 5 ) as ( (3m^2 - 5) = (3m - \sqrt{5})(3m + \sqrt{5}) ), and ( m^2 - 4 ) as ( (m^2 - 4) = (m - 2)(m + 2) ).

Therefore, the expression ( -6m^5 + 34m^3 - 40m ) can be factored completely as:

[ 2m(3m - \sqrt{5})(3m + \sqrt{5})(m - 2)(m + 2) ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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