Question

When factored completely,x³-13x²-30x is

Answer 1

`x(x+2)(x-15)`

Explanation:

we have

`x^(3)-13x^(2)-30x`

step 1

Factor x

`x^(3)-13x^(2)-30x=x(x^(2)-13x-30)`

step 2

Find the solutions of
`(x^(2)-13x-30)`

Complete the square

`(x^(2)-13x)=30`

`(x^(2)-13x+6.5^(2))=30+6.5^(2)`

`(x^(2)-13x+42.25)=72.25`

`(x-6.5)^(2)=72.25`

square root both sides

`(x-6.5)=(+/-)8.5`

`x=6.5(+/-)8.5`

`x1=6.5(+)8.5=15`

`x2=6.5(-)8.5=-2`

so

`(x^(2)-13x-30)=(x+2)(x-15)`

substitute

`x^(3)-13x^(2)-30x=x(x+2)(x-15)`