Question

What are the possible integral zeros of `P(x)=x^3+3x^2-6x-8`?

Answer 1

`x=-4,x=-1" and "x=2`

Explanation:

`"note that "`

`f(2)=8+12-12-8=0`

`rArr(x-2)" is a factor"`

`color(red)(x^2)(x-2)color(magenta)(+2x^2)+3x^2-6x-8`

`=color(red)(x^2)(x-2)color(red)(+5x)(x-2)color(magenta)(+10x)-6x-8`

`=color(red)(x^2)(x-2)color(red)(+5x)(x-2)color(red)(+4)(x-2)cancel(color(magenta)(+8))cancel(-8)`

`rArrx^3+3x^2-6x-8`

`=(x-2)(x^2+5x+4)`

`=(x-2)(x+1)(x+4)=0`

`rArrx=-4,x=-1" and "x=2larrcolor(blue)"are the zeros"`