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
Algebra II - Jessica, Thursday, September 22, 2011 at 3:17pm
the first step should be x^2+2x-2x-4 = x^2-4(I forgot to put the (-4)
Algebra II - Steve, Thursday, September 22, 2011 at 3:47pm
So far, so good.
(x^2-4)(x-4) = x^3 - 4x^2 - 4x + 16
You don't need an equation, just the polynomial.
Algebra II-Please recheck - Jessica, Thursday, September 22, 2011 at 4:31pm
Is that in simplest form or am I suppose to do something else with it? It seems too easy-
The polynomial you have written is indeed in its simplest form. There is no further simplification or expansion needed. So, you have correctly simplified the polynomial.
To write a polynomial in simplest form when given the roots, you need to start by using the roots to create factors of the polynomial. In this case, the roots are 2, -2, and 4.
To remove the parentheses, you need to multiply out the factors. Here's the correct way to do it:
Step 1: Start with the original problem: (x-2)(x+2)(x-4)
Step 2: Multiply the first two factors using the distributive property:
(x-2)(x+2) = x^2 + 2x - 2x - 4 = x^2 - 4
Step 3: Multiply the result from step 2 with the third factor:
(x^2 - 4)(x-4) = x^3 - 4x^2 - 4x + 16
So, your final polynomial in simplest form is x^3 - 4x^2 - 4x + 16.
You have correctly multiplied out the factors and simplified the polynomial. It is in the simplest form and does not require any further simplification.
If you have any more questions or need further assistance, feel free to ask.