Question #c44e8

1 Answer
Jim G.
Nov 23, 2017

#x=-1,x=2,x=4#

Explanation:

#"given that "x=-1" is a root"#

#"then "(x+1)" is a factor"#

#color(red)(x^2)(x+1)color(magenta)(-x^2)-5x^2+2x+8#

#=color(red)(x^2)(x+1)color(red)(-6x)(x+1)color(magenta)(+6x)+2x+8#

#=color(red)(x^2)(x+1)color(red)(-6x)(x+1)color(red)(+8)(x+1)cancel(color(magenta)(-8))cancel(+8)#

#=color(red)(x^2)(x+1)color(red)(-6x)(x+1)color(red)(+8)(x+1)+0#

#rArr(x^2-6x+8)(x+1)=0#

#rArr(x-2)(x-4)(x+1)=0#

#"equate each factor to zero and solve for x"#

#x-2=0rArrx=2#

#x-4=0rArrx=4#

#x+1=0rArrx=-1#

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