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Is your LCM a multiple of expression (1)? YesFind 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 (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?

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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?

The LCM of 12 and 16 is 48 or 3(4)^2.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?

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Yes!

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Feeling good about the last couple of questions. Hopefully, I'll not forget how to do this by the time I reach the end of the textbook.Yes!

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