find all the zero's of the followig polynomial. write the polynomial in form.
f(x)=x^2-256
should be
f(x)=x^4-256
x^4-256
(x^2-16)(x^2+16)
(x-4)(x+4)(x^2+16)
that should make it clear.
As soon as I posted that I saw at the bottom the realted questions where someone had posted the same question back in August. Yes, it does. Thanks!!
To find the zeros of a polynomial, we need to solve the equation when the polynomial is equal to zero. In this case, we have the polynomial f(x) = x^2 - 256.
To find the zeros, we set the polynomial equal to zero:
x^2 - 256 = 0
To solve this quadratic equation, we can use the fact that it can be factored as a difference of squares. The difference of squares formula states that a^2 - b^2 can be factored as (a - b)(a + b). In our case, a is x and b is 16:
(x - 16)(x + 16) = 0
Now we have two equations:
x - 16 = 0 or x + 16 = 0
Solving each equation gives us the values of x:
For x - 16 = 0, adding 16 to both sides gives:
x = 16
For x + 16 = 0, subtracting 16 from both sides gives:
x = -16
Therefore, the zeros of the polynomial f(x) = x^2 - 256 are x = 16 and x = -16.
To write the polynomial in factored form, we use the zeros we found:
f(x) = (x - 16)(x + 16)