How do you find the LCM of #x^8 12x^7 +36x^6, 3x^2 108# and #7x+ 42#?
The LCM is:
#21x^9126x^8756x^7+4536x^6#
For this question, it's probably easiest to factor all of the polynomials first:
The simplest product of polynomial factors including all of the linear factors we have found, in their multiplicities is:
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To find the least common multiple (LCM) of the given expressions, we need to factorize each expression and then determine the highest power of each factor that appears in any of the expressions.
The given expressions are:

x^8  12x^7 + 36x^6

3x^2  108

7x + 42

Factoring x^8  12x^7 + 36x^6: x^8  12x^7 + 36x^6 = x^6(x^2  12x + 36) = x^6(x  6)^2

Factoring 3x^2  108: 3x^2  108 = 3(x^2  36) = 3(x  6)(x + 6)

Factoring 7x + 42: 7x + 42 = 7(x + 6)
Now, we determine the highest power of each factor that appears in any of the expressions:
 The factor x^6 appears in the first expression.
 The factors (x  6) and (x + 6) appear in the second expression.
 The factor (x + 6) appears in the third expression.
Therefore, the LCM of x^8  12x^7 + 36x^6, 3x^2  108, and 7x + 42 is: x^6(x  6)(x + 6)
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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