Question 300765
Given: {{{M^3 - 10M^2 +25M}}}
First you can factor out an M
{{{M*(M^2 - 10M + 25)}}}
Now you need to factor {{{M^2 - 10M + 25}}}
This can be done by unfoiling the equation
Find the factors of 25: 1,5,5,25
After you find those factors you need to see what adds together to get -10
-5 - 5 = -10
Your equation now becomes {{{M - 5)*(M - 5)}}}
But that was just the part inside the parenthesis
The complete factored equation is: {{{highlight(M*(M-5)*(M-5))}}}
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You can also solve for M by setting the equation to 0
Then you can solve for each term.
Since we started with an M^3, there will be 3 answers
(The number of answers is determined by the highest exponent (in this problem it was 3))
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{{{highlight(M = 0)}}}
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{{{M - 5 = 0}}}
{{{highlight_green(M = 5)}}}
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{{{M - 5 = 0}}}
{{{highlight(M = 5)}}}
And yes you can have the same answer more than once