Question

If I have x^5 -81x and I want to find all the zeros here is how I go about that: x(x^4-81), x(x^4-3^4), x((x^2)^2-(3^2)^2), x((x^2-3^2)(x^2+3^2), x((x-3)(x+3)(x+3i)(x-3i))

I am confused as whether the parentheses separating the (alone) x from the rest of the equation are necessary. For example -1(3*10), distribute the negative one is +30, but if I do what is in the parentheses first I get -30. I know the associative property and cumulative property as I understand them.

Answer 1

-1(3*10) = -30
it cannot be +30
distribution happens in addition/subtraction to multiplication, like a(b+c) = ac+ac

Answer 2

Thanks a ton, could you expand a little bit if possible on how that relates to the polynomial above.

Answer 3

what you have done is correct
x^5-81x= x((x-3)(x+3)(x+3i)(x-3i))
so zeros are 0,3,-3,3i,-3i

Answer 4

I think I am confused because there is addition, subtraction, and multiplication inside the parentheses in the above polynomial.

Answer 5

all the steps are correct, which step u have doubt in particular ?

Answer 6

The need for all the parenthesis in the final step.

Answer 7

yes, that paranthesis is needed
x(x^4+81) must be there.

Answer 8

Will you expand on that a little. I still feel stuck for some reason.

Answer 9

Its not quite clear. I understand the difference now between -1(3+10) and -1(3*10)

Answer 10

@hartnn

Answer 11

x^5-81x= x.x^4-81x
Taking x common
=x(x^4-81)
if u don't put paranthesis , u will have x.x^4-81 which is x^5-81 which is incorrect

Answer 12

Oh thanks that make a lot of sense.

Answer 13

glad i could clear it :)