LCM of Polynomial Functions 1

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mathdad

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Find the LCM of the given polynomials.


x^2 - x - 12; x^2 - 8x + 16

Solution:

x^2 - x - 12 = (x - 4) (x + 3)

x^2 - 8x + 16 = (x - 4) (x - 4)

LCM = (x - 4) (x + 3)

Yes?
 
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Harry_the_cat

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Find the LCM of the given polynomials.

x^2 - x - 12; x^2 - 8x + 16

Solution:

x^2 - x - 12 = (x - 4) (x + 3) … Let's call this expression (1)

x^2 - 8x + 16 = (x - 4) (x - 4) … Let's call this expression (2)

LCM = (x - 4) (x + 3)

Yes?
Is your LCM a multiple of expression (1)? Yes
Is your LCM a multiple of expression (2)? No! So it can't be the LCM if its not even a multiple.

Consider this:
12 = 4*3
16 = 4*4
What is the LCM of 12 and 16? Is it 4*3? Or is it 4*4*3?
 

mathdad

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Is your LCM a multiple of expression (1)? Yes
Is your LCM a multiple of expression (2)? No! So it can't be the LCM if its not even a multiple.

Consider this:
12 = 4*3
16 = 4*4
What is the LCM of 12 and 16? Is it 4*3? Or is it 4*4*3?
Is your LCM a multiple of expression (1)? Yes
Is your LCM a multiple of expression (2)? No! So it can't be the LCM if its not even a multiple.

Consider this:
12 = 4*3
16 = 4*4
What is the LCM of 12 and 16? Is it 4*3? Or is it 4*4*3?
The LCM of 12 and 16 is 48 or 3(4)^2.
 

mathdad

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Going back to my original question, see below.

x^2 - x - 12; x^2 - 8x + 16

Solution:

x^2 - x - 12 = (x - 4) (x + 3)

x^2 - 8x + 16 = (x - 4) (x - 4)

LCM = (x - 4)^2(x + 3)

Yes?
 

Harry_the_cat

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Yes!
 

mathdad

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