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

1 Answer
Jim G.
Jan 5, 2018

#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"#

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