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 (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?
Yes!