How can you convert this #x^3-x^2-x+1# into #(x-a)(x-b)(x-c)# ?

Is there any formula to convert this #x^3-x^2-x+1# into #(x-a)(x-b)(x-c)#.
If available please help me.

2 Answers
Harish Chandra Rajpoot
Jul 26, 2018

#(x-1)(x-1)(x+1)#

Explanation:

Given cubic polynomial:

#x^3-x^2-x+1#

#=x^2(x-1)-(x-1)#

#=(x-1)(x^2-1)#

#=(x-1)(x-1)(x+1)#

Jim G.
Jul 26, 2018

#x-1)(x-1)(x+1)#

Explanation:

#"note the sum of the coefficients"#

#1-1-1+1=0#

#"Thus "x=1" is a zero and "(x-1)" is a factor"#

#"dividing "x^3-x^2-x+1" by "(x-1)" gives"#

#(x-1)(x^2-1)#

#=(x-1)(x-1)(x+1)#

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