Question

Determine which binomial factor of -2x^3+14x^2-24x+20. Show your workA) x+5B) x+20C) x-24D) x-5

Answer 1

`-2x^3+14x^2-24x+20`

Factor -2 out:

`-2(x^3-7x^2+12x-10)`

The divisors of 10 are:

`1,2,5,10`

Therefore, the possible rational roots of the:

`x^3-7x^2+12x-10`

are:

`\begin{gathered} x=\pm1 \\ x=\pm2 \\ x=\pm5 \\ x=\pm10 \end{gathered}`

so:

This gives x - 5 as all linear factors:

`-2((x-5)(x^3-7x^2+12x-10))/((x-5))`

Therefore, the binomial factor is:

`(x-5)`