Question

How do you solve `x^3 - 10x^2 +24x = 0`?

Answer 1

`x=0 or 4 or 6`

Explanation:

`x^3-10x^2+24x=0`

Factor,

`x(x^2-10x+24)=0`

Factor,

`x(x-6)(x-4)=0`

Hence,

`x=0 or 4 or 6`

Answer 2

`x=0,x=4,x=6`

Explanation:

`"take out a "color(blue)"common factor " x`

`x(x^2-10x+24)=0`

`"the factors of + 24 which sum to - 10 are - 4 and - 6"`

`rArrx(x-4)(x-6)=0`

`"equate each factor to zero and solve for x"`

`rArrx=0`

`rArrx-4=0rArrx=4`

`x-6=0rArrx=6`