N/A Factoring N/A
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MAKG1
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MAKG
Homework, eh?
What are the factors for the highest and lowest terms?
There are only so many ways to put them together.
What are the factors for the highest and lowest terms?
There are only so many ways to put them together.
Last edited:
JB1842
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jimhorner
Line Up and Wait
Quadratic formula!
Given: ax^2 + bx + c
x = (-b +/- sqrt(b^2 - 4ac))/2a
So, for your formula: 9m^2 (2m^2 +6m -1)
you already have factors of 9m and m, the problem is to factor
2m^2 +6m -1
Using the quadratic formula:
a=2, b=6, c=-1
x = (-6 +/- sqrt (6^2 - 4(2)(-1)))/(2*2)
x = -6/4 +- sqrt (44)/4
x = -3/2 +- 1/2sqrt(11)
writing as factors:
(x+3/2+sqrt(11)/2)(x+3/2-sqrt(11)/2)
multiplying that out gives (2x^2 + 6x -1)/2
Final answer in factored form:
(18)(m)(m)(m+3/2+sqrt(11)/2)(m+3/2-sqrt(11)/2)
QED!
BTW, the roots or zero crossings are:
m=0
m=-3/2 + sqrt(11)/2
m=-3/2 - sqrt(11)/2
The sqrt(11) means that it would have been very difficult to do the simple factoring into (x+something)(x+somethingelse). I'm surprised that this was given as a factoring problem because the quadratic formula was required to solve it. Is it possible that there is an error in how the original problem was entered?
Given: ax^2 + bx + c
x = (-b +/- sqrt(b^2 - 4ac))/2a
So, for your formula: 9m^2 (2m^2 +6m -1)
you already have factors of 9m and m, the problem is to factor
2m^2 +6m -1
Using the quadratic formula:
a=2, b=6, c=-1
x = (-6 +/- sqrt (6^2 - 4(2)(-1)))/(2*2)
x = -6/4 +- sqrt (44)/4
x = -3/2 +- 1/2sqrt(11)
writing as factors:
(x+3/2+sqrt(11)/2)(x+3/2-sqrt(11)/2)
multiplying that out gives (2x^2 + 6x -1)/2
Final answer in factored form:
(18)(m)(m)(m+3/2+sqrt(11)/2)(m+3/2-sqrt(11)/2)
QED!
BTW, the roots or zero crossings are:
m=0
m=-3/2 + sqrt(11)/2
m=-3/2 - sqrt(11)/2
The sqrt(11) means that it would have been very difficult to do the simple factoring into (x+something)(x+somethingelse). I'm surprised that this was given as a factoring problem because the quadratic formula was required to solve it. Is it possible that there is an error in how the original problem was entered?
Last edited:
Terry
Line Up and Wait
Jim, No, the problem is correct. The daughter and I was looking through her new math book. She is working on her degree and I just grabbed the problem from the book and tried to factor it first.
When I went to the "Problem Solving" site and entered just the (2m^2+6m-1) , it dawned on me it was a Quadratic.
I then solved the problem just like you did above but figured no one was interested, so I didn't say anything.
I felt sort of embarrassed for posting without thinking it through.
Anyway, thanks for the help.
Terry