SOLUTION: Factor each of the following trinomial completely please with a step by step explanation so I can understand what you did and how you did it. Thank You 2a^3

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Question 83585: Factor each of the following trinomial completely please with a step by step explanation so I can understand what you did and how you did it. Thank You
2a^3 - 52a^2 b + 96ab^2
Found 2 solutions by uma, ankor@dixie-net.com:
Answer by uma(370) (Show Source):
You can put this solution on YOUR website!
The given expression is 2a^3-52a^2b+96ab^2
As a is common to all the terms, remove it out.
= a(2a^2 - 52ab + 96b^2)
Now find 2 numbers whose product = 2 x 96 = 192 and whose sum = - 52
On trying out, w find the numbers as - 48 and - 4
= a(2a^2 - 4ab - 48ab + 96 b^2) [splitting the middle term]
= a[2a(a - 2b) - 48b(a - 2b)]
= a(a - 2b) ( 2a - 48b)
= a(a - 2b)*2(a - 24 b)
= 2a(a - 2b)(a - 24b)

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Factor each of the following trinomial completely please with a step by step explanation so I can understand what you did and how you did it. Thank You
2a^3 - 52a^2b + 96 ab^2
:
Factor out 2a from each term, we then have:
2a(a^2 - 26ab + 48b^2)
:
(a^2 - 26ab + 48b^2) can be factored to (a-24)(a-2) so we have:
:
2a(a - 24b)(a - 2b)
:
Note on factoring:
Since the last term is positive we know that the factors will have the same sign
Since the middle term is negative we know that both will be negative
Find the two factors of 48 that will add up to the middle term (26) 2 + 24 but here it would -2b * -24b
:
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SOLUTION: Factor each of the following trinomial completely please with a step by step explanation so I can understand what you did and how you did it. Thank You 2a^3 - 52a^2 b + 96ab^2