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

Question

mathstudent55 · Answer

I don't understand what is the GCF of one polynomial. 
The GCF is the greatest common factor of 2 or more numbers or polynomials.

Start with the factors:
x, x + 1, x - 2
Now multiply them together.
$x(x + 1)(x - 2) $

$= (x^2 + x)(x - 2) $

$= x^3 - 2x^2 + x^2 - 2x$

$=x^3 - x^2 - 2x$

Our polynomial is: $x^3 - x^2 - 2x$

Since we created our own polynomial from factors, now we know that this polynomial factors as

$x^3 - x^2 - 2x = x(x + 1)(x - 2)$

You can combine x with x + 1, and later x with x - 2, and have two other forms of the polynomial:

$x^3 - x^2 - 2x = (x^2 + x)(x - 2)$

$x^3 - x^2 - 2x = (x^2 - 2x)(x + 1)$

help_people · Answer

muchos gracias thank you so so much.

help_people · Answer

^ @mathstudent55

mathstudent55 · Answer

You're welcome.