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, $a = 1/2 or 1/4$

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