Question

Is (x-2) a factor of y=-1(x^3-5x^2+6x-30)(x^2-16)

Answer 1

Polynomials

We are factoring

`y=-(x^3-5x^2+6x-30)(x^2-16)`

We know

`(x^2-16)=(x-4)(x+4)`
`\begin{gathered} x^3-5x^2+6x-30=x^2(x-5)^{}+6(x-5) \\ =(x-5)(x^2+6) \end{gathered}`

Then

`y=-(x-5)(x^2+6)(x^{}-4)(x+4)`

Then (x - 2) is not a factor of y