Question

Need Help Asap!!!

Answer 1

I can do it, but then it will be my polynomial.  I suggest you repeat these steps with different numbers.

Let's pick a couple of zeros for our polynomial and a scale factor, how about 2, -1 and 3?

So our polynomial is

$3(x - 2)(x + 1) = (3x - 6)(x+1) = (x-2)(3x+3)= 3(x^2-x-2) = 3x^2 - 3x - 6$

That's five forms all together, two bonus forms!

I forgot to explain:  Once we wrote the polynomial as the product of three factors, we can multiply any pair of factors to get an equivalent polynomial; that's three right there, and one more for multiplying it out entirely.

Answer 2

We'll use the following terms:

x, (x + 2), (x + 4)

Multiply the terms together to get your factorable polynomial:

$x \times (x + 2) = (x \times x) + (x \times 2) = x^2 + 2x$

$(x^2 + 2x) \times (x \times 2) = x^3 + 6x^2 + 8x$

The polynomial we have created will be x^3 + 6x^2 + 8x.

We can rewrite this polynomial by taking out one of the terms we used to multiply for said polynomial:

$\text{Taking out (x)}$
$x^3 + 6x^2 + 8x = x(x^2 + 6x + 8)$

This was achieved by taking out x from each term, and moving x outside the parentheses.

$\text{Taking out (x+2)}$
$x^3 + 6x^2 + 8x = (x+2)(x^2 + 4x)$

This was achieved through long division, which is shown in the attached picture below.

You can find the GCF of the polynomial by finding the biggest number that divides into each term:

$\text{GCF of } (x^3 + 6x^2 + 8x) = x$

The GCF of this polynomial will be x.