find the l. c. m of 2x^3+2x^2-12x,6x^3-6x^2-72x, 4x^3-24x^2+32x
Answers
Answer:
We know that LCM is the least common multiple.
Factorise 4x
3
+4x
2
−x−1 as follows:
4x
3
+4x
2
−x−1=4x
2
(x+1)−1(x+1)=(4x
2
−1)(x+1)=[(2x)
2
−1
2
](x+1)=(2x+1)(2x−1)(x+1) (using identity a
2
−b
2
=(a+b)(a−b))
Now, factorise 8x
3
−1 as follows:
8x
3
−1=(2x)
3
−1
3
=(2x−1)[(2x)
2
+1+2x]=(2x−1)(4x
2
+1+2x)
(using identity a
3
−b
3
=(a−b)(a
2
+b
2
+ab))
Finally, factorise 8x
2
−2x−1 as follows:
8x
2
−2x−1=8x
2
−4x+2x−1=4x(2x−1)+1(2x−1)=(4x+1)(2x−1)
Therefore, the least common multiple between the polynomials 4x
3
+4x
2
−x−1, 8x
3
−1 and 8x
2
−2x−1 is:
LCM=(2x+1)×(2x−1)×(x+1)×(4x
2
+1+2x)×(4x+1)
=(x+1)(2x+1)(4x+1)[(2x−1)(4x
2
+1+2x)]
=(x+1)(2x+1)(4x+1)(8x
3
−1) (using identity a
3
−b
3
=(a−b)(a
2
+b
2
+ab))
Hence, the LCM is (x+1)(2x+1)(4x+1)(8x
3
−
1).
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Step-by-step explanation:
Force is the external factor that changes or attempts to change the state of an object in a pause or a state of motion, or in the shape or shape of an object.