Question

How do you solve the polynomial `10x^3-5x^2=0`?

Answer 1

In order to solve the algebraic equation for the variable x we would begin by factoring out the common factor from the equation
`10x^3 - 5x^2 = 0`
The common factor between `10x^3` and `5x^2` is `5x^2`

`5x^2(2x -1) = 0`

Next we would set each value of x equal to 0

`5x^2 = 0 and (2x -1) = 0`

`5x^2 = 0` divide by 5 and square root each side
`x^2 = 0/5`
`x= 0`

`(2x -1) = 0` add 1 and divide by 2 on each side
`2x = 0 + 1`
`x = 1/2`

`x = {0 , 1/2}`