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

Talamancoeb 2021-12-18 Answered
Find the LCM of the given polynomial.
x2+4x+4,x3+2x2,(x+2)3
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Expert Answer

twineg4
Answered 2021-12-19 Author has 33 answers
Step 1
The given polynomials are,
x2+4x+4,
x3+2x2,
(x+2)3
We need to find the LCM of the given polynomials.
Step 2
On factorizing the first polynomial, we get
x2+4x+4=x2+2x2+22
=(x+2)2
On factorizing the second polynomial, we get
x3+2x2=x2(x+2)
And the third polynomial is (x+2)3
The lowest common multiple of the three polynomials is the polynomial which is multiple of the given three polynomials,
Therefore, the LCM of the polynomials is x2(x+2)3

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