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:

$-2\frac{(x-5)(x^3-7x^2+12x-10)}{(x-5)}$

Therefore, the binomial factor is:

$(x-5)$