Determine The Value Of #a# So That When #P(x) = (a^2)(x^3)-3ax+1# Is Divided By #x-2# There Is No Remainder. Help, Please?

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Answer 1 · 2018-03-02T16:48:53

when divided by #x-2#, there is no remainder, hence #x=2# is the solution.

That is, when you plug in #x=2# in #a^2x^3−3ax+1#, it would be equal to 0.

#2^3a^2 −3(2)a+1=0#

#8a^2 −6a+1=0#

#8a^2 −4a -2a+1=0#

#4a(2a −1) -1(2a-1)=0#

#(4a-1)(2a-1)=0#

Therefore, #a = 1/2 or 1/4#