I need to write a polynomial in SIMPLEST FORM having roots 2,-2 and 4. I have to gt rid of the parentheses by multiplying everything out.Did I do it correctly? Also, someone said yes, but I'm wondering if it suppose to have anything else done to it-it seems way too easy the way I did it.

Question

I need to write a polynomial in SIMPLEST FORM having roots 2,-2 and 4. I have to gt rid of the parentheses by multiplying everything out.Did I do it correctly? Also, someone said yes, but I'm wondering if it suppose to have anything else done to it-it seems way too easy the way I did it.

(x-2)(x+2)(x-4)original problem
1.x^2 + 2x-2x=x^2-4)
2. (x^2-4)(x-4)
3. x^3-4x^2-4x+16=0

Answer 1

To write the polynomial in its simplest form, you need to correctly expand the expression (x-2)(x+2)(x-4) without any parentheses.

Here's how you can multiply everything out step by step:

1. Start by multiplying the first two factors:
(x - 2)(x + 2) = x * x + x * 2 - 2 * x - 2 * 2
= x^2 + 2x - 2x - 4
= x^2 - 4

2. Next, multiply the expression (x^2 - 4) by the third factor:
(x^2 - 4)(x - 4) = x^2 * x + x^2 * (-4) - 4 * x + (-4) * (-4)
= x^3 - 4x^2 - 4x + 16

So, the correct expression after multiplying everything out is:
x^3 - 4x^2 - 4x + 16 = 0

According to your steps, it appears that you've correctly expanded and multiplied everything out. Your final expression, x^3 - 4x^2 - 4x + 16 = 0, is indeed the simplest form polynomial. It's always good to double-check your work, especially when it seems too easy. In this case, you can confidently say that you've done it correctly.