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Create a factorable polynomial with a GCF of 3x. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.

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Answer:

Create a factorable polynomial with a GCF of 3x. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)

My answer:

6x^3 + 39x^2 + 60x

two other equivalent forms:

1.  3x(x+4)(5+2x)

2.   3x(2x^2 + 13x +20)

1st- Here's how I got the first equation. I just choose 2 random binomial factors off the top of my head and had them be multiplied with 3x since it's the GCF.

2nd- Here's how I got the second equation. Using the last equation, 3x(x+4)(5+2x), I just multiplied (x+4) with (5+2x) which equals 2x^2 + 13x + 20.

I actually got help from my teacher for this so I know it's right. Really hope this helps because I was also having trouble with this :)

The factorable polynomial with a Greatest common factor of [tex]3x[/tex] will be[tex]6x^3 + 39x^2 + 60x[/tex] and its two other forms are [tex](A)[/tex]  [tex]3x(2x^2 + 13x + 30)[/tex] and [tex](B)[/tex]  [tex]3x(x+4)(2x+5)[/tex].

What is Greatest common factor ?

Greatest common factor is the largest factor that all the numbers have in common.

We have,

The factorable polynomial should have Greatest common factor of [tex]3x[/tex].

So,

Let a polynomial [tex]6x^3 + 39x^2 + 60x[/tex],

Now find its factor;

[tex]6x^3 + 39x^2 + 60x[/tex]

Taking [tex]3[/tex] common,

[tex]3(2x^3 + 13x^2 + 30x)[/tex]

Now, Taking [tex]x[/tex] common,

[tex]3x(2x^2 + 13x + 30)[/tex]

Now we have Quadratic equation now find its factor;

We get,

[tex]3x(x+4)(2x+5)[/tex]

So, this is the polynomial with Greatest common factor.

Now,

So two other equivalent form of this polynomial are;

[tex](A)[/tex]  [tex]3x(2x^2 + 13x + 30)[/tex]

[tex](B)[/tex]  [tex]3x(x+4)(2x+5)[/tex]

The explanation has been done while finding the factors.

Hence, we can say that the factorable polynomial with a Greatest common factor of [tex]3x[/tex]  are [tex]6x^3 + 39x^2 + 60x[/tex] and its two other forms are [tex](A)[/tex]  [tex]3x(2x^2 + 13x + 30)[/tex] and [tex](B)[/tex]  [tex]3x(x+4)(2x+5)[/tex].

To know more about Greatest common factor click here

https://brainly.com/question/27325672

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