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sologuitar

Member

Registered: 2022-09-19

Posts: 467

LCM of Polynomials...2

Find the LCM of the given polynomial.

x^2 + 4x + 4, x^3 + 2x^2, (x + 2)^3

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: LCM of Polynomials...2

Hopefully you have done the earlier one by now so you have a good idea what to do.

(1) factorise all the expressions.
(2) build a new expression by including all the factors but leaving out repeats of common factors.

Post an attempt and I'll check it.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: LCM of Polynomials...2

Hopefully you have done the earlier one by now so you have a good idea what to do.

(1) factorise all the expressions.
(2) build a new expression by including all the factors but leaving out repeats of common factors.

Post an attempt and I'll check it.

Bob

Let me see.

x^2 + 4x + 4, x^3 + 2x^2, (x + 2)^3

Factoring x^2 + 4x + 4, I get (x + 2)(x + 2).

Factoring x^3 + 2x^2, I get x^2(x + 2).

(x + 2)^3 = (x + 2)(x + 2)(x + 2).

From the first group, I take one (x + 2).

From the second group, I take x^2 and (x + 2).

From the third group, I take two (x + 2)(x + 2) because there are 3 of the same.

We put it all together.

My answer is (x + 2)(x^2)(x + 2)(x + 2)^2.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: LCM of Polynomials...2

You've got too many (x+2).

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: LCM of Polynomials...2

You've got too many (x+2).

What about removing one (x + 2)?

(x + 2)(x^2)(x + 2)^2.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: LCM of Polynomials...2

That's it!  I would write like this:  x^2(x+2)^3

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: LCM of Polynomials...2

That's it!  I would write like this:  x^2(x+2)^3

Bob

Very good. I will practice more of these LCM problems. I think they are very important.