Find the LCM of the given polynomial. 4x3−4x2+x,2x3−x2,x3

Question

Find the LCM of the given polynomial.  4x3−4x2+x,2x3−x2,x3

twineg4 · Accepted Answer

Step 1: Given  4x3−4x2+x,2x3−x2,x3  Step 2: Solution  Factoring them  4x3−4x2+x=x(2x−1)22x3−x2=x2(2x−1)  x3  LCM is the product of all the factors which are common, and which are not common  So LCM is  x3(2x−1)2  Answer:  x3(2x−1)2

Mollie Nash · Accepted Answer

for the first one,it&#039;s x(4x2−4x+1)⇒x(2x−1)(2x−1)for the second one,x2(2x−1)for the third one,x3hence lcm for these three is just x

Vasquez · Accepted Answer

You have to factor each polynomial first;
$\begin{matrix} 4 x^{3} - 4 x^{2} + x = x (2 x - 1)^{2} \\ 2 x^{3} - x^{2} = x^{2} (2 x - 1) \\ x^{3} = x^{3} \end{matrix}$
Then we see we need to have a total of two (2x-1) factors, since the highest power is 2, and three x factors, since the highest power is 3. The Least Common Multiple is then $x^{3} (2 x - 1)^{2} = 4 x^{5} - 4 x^{4} + x^{3} .$

Find the LCM of the given polynomial. 4x^{3}-4x^{2}+x, 2x^{3}-x^{2}, x^{3}

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