Talamancoeb

2021-12-18

Find the LCM of the given polynomial.

$x}^{2}+4x+4,{x}^{3}+2{x}^{2},{(x+2)}^{3$

twineg4

Beginner2021-12-19Added 33 answers

Step 1

The given polynomials are,

${x}^{2}+4x+4,$

${x}^{3}+2{x}^{2},$

$(x+2)}^{3$

We need to find the LCM of the given polynomials.

Step 2

On factorizing the first polynomial, we get

$x}^{2}+4x+4={x}^{2}+2x\cdot 2+{2}^{2$

$={(x+2)}^{2}$

On factorizing the second polynomial, we get

${x}^{3}+2{x}^{2}={x}^{2}(x+2)$

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$x}^{2}{(x+2)}^{3$

The given polynomials are,

We need to find the LCM of the given polynomials.

Step 2

On factorizing the first polynomial, we get

On factorizing the second polynomial, we get

And the third polynomial is

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

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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