Question 28143: Question: Use a method to determine the LCM for
(9x^3-9x^2-18x) and (6x^5-24x^4+24x^3)
What is the LCM?
Please help! Thank you! Answer by sdmmadam@yahoo.com(530) (Show Source):
You can put this solution on YOUR website! Question: Use a method to determine the LCM for
(9x^3-9x^2-18x) and (6x^5-24x^4+24x^3)
What is the LCM?
(9x^3-9x^2-18x)----(1)
=9x(x^2-x-2)
=9x(x-2)(x+1)----(*)(on factorising)
(6x^5-24x^4+24x^3)----(2)
=6x^3(x^2-4x+4)
=6x^3(x-2)(x-2)----(**)(on factorising)
lcm of (1) and (2) is lcm of (*) and (**)
Therefore lcm of 9x(x-2)(x+1)and 6x^3(x-2)(x-2)is given by
18x^3(x+1)(x-2)^2
Answer:18x^3(x+1)(x-2)^2
Note: How?
the lcm of x and x^3 is x^3
the lcm of 9=3X3 and 6=2X3 is 3X2X3 = 18
(the common factor 3 and then the loose factor 3 of the first and the loose factor 2 of the second)
Similarly for the lcm of (x-2)(x+1)and (x-2)(x-2)(the common factor (x-2) and then the loose factor (x+1)of the first and the loose factor (x-2) of the second)
Note:
(x^2-x-2)=[x^2+(-2x+x)-2]
[splitting the mid term into two parts in such a way that their sum is the mid term and their product is the product of the square term and the constant term.
Now -x= +(-2x+x) and (-2x)X(x) = -2x^2 = (x^2)X(-2)]
=[(x^2-2x)+(x-2)]
=[x(x-2)+1(x-2)]
=[xp+p](where p = (x-2)}
=p(x+1)
=(x-2)(x+1)
Note:(x^2-4x+4)
= (x)^2-2(x)(2) + (2)^2 [in the form (a)^2 -2ab+(b)^2 = (a-b)^2]
=(x-2)^2
=(x-2)(x-2)
You may factorise in the first note form method too.
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