How do you determine whether x-1 is a factor of the polynomial #2x^3-x^2-3x-2#?

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Answer 1 · 2017-02-02T07:12:18

#(x-1)# is not a factor

We use the remainder theorem

When we divide a polynomial #f(x)# by #(x-c)#,

#f(x)=(x-c)q(x)+r(x)#

When #x=c#

#f(c)=r#

If #(x-c)# is a factor #f(c)=0#

So, here

#f(x)=2x^3-x^2-3x-2#

#f(1)=2-1-3-2=-4#

Therefore,

the remainder is #=-4#

So, #(x-1)# is not a factor of #f(x)#