Question 72957: m^3+2m^2-3m=0 Solve each equation so Far i have
M(M^2+2m-3)=0 Found 2 solutions by funmath, bucky:Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website! m^3+2m^2-3m=0
M(M^2+2m-3)=0
Good start, now finish factoring.
m(m____)(m___)=0
fill the blanks with two integers that multiply to give you the last term, -3, but add to give you the middle coefficient, +2.
3*-1=-3 and 3+(-1)=+2
m(m+3)(m-1)=0
Set each factor equal to 0 and solve:
m=0 or m+3=0 or m-1=0
m=0 or m+3-3=0-3 or m-1+1=0+1
m=0 or m=-3 or m=1
Happy Calculating!!!!!
You can put this solution on YOUR website!
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So far you are correct.
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The next thing you can do is notice that the term can be factored. It
factors into .
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Now you can return to your equation and substitute these factors for and
you will then have:
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Notice that this equation will be true if any of the factors on the left side equals zero.
This is because a zero factor on the left side is a multiplier and it will make the whole
left side equal to zero which is also the right side. Therefore, with a zero factor the
equation is balanced because 0 equals 0 is the result.
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So all you have to do is set each of the three factors equal to zero and solve for m.
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The first factor is m and setting it equal to zero says: . This becomes one
of the answers.
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The second factor is and setting it equal to zero results in: . You
can solve for m by subtracting +3 from both sides to get rid of the +3 on the left side.
When you subtract +3 from both sides you get and that is the second answer.
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Finally, the third factor is and setting it equal to zero gives you the equation . You can solve this equation for m by adding 1 to both sides to eliminate the
-1 on the left side. Adding +1 to both sides of this equation results in .
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So the three possible answers for m are 0, -3, and +1. Each of these three can be substituted
back into the original equation given in the problem, and that equation will become
equal on both sides.
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I hope this helps you understand the problem a little more. The hardest part of this problem
was to recognize that you could factor the quadratic terms and then to find the factors. It
takes a lot of practice to do this and you are well on your way to getting it. Keep up the
good work!
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