How do you use the factor theorem to determine whether x-4 is a factor of #x^3-21x+20#?

1 Answer
KillerBunny
Nov 16, 2015

The factor theorem states that if #f(x_0)=0#, then #(x-x_0)# divides #f(x)#. So, #(x-4)# divides #x^3-21x+20# if and only if the polynomial is zero when #x=4#.

Let's do the computation:

#f(4)= 4^3 - 21*4+20 = 64-84+20 = 0#

So yes, #(x-4)# is a factor of #x^3-21x+20#. Indeed, the three roots are #-5#, #1# and #4#, so we have

#x^3-21x+20=(x-1)(x-4)(x+5)#

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