Solution to Express 3x 4 +4x 3 +2x 2 +x in terms of [x]4,[x]3,[x]2 and [x]. - Sikademy
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Archangel Macsika

Express 3x 4 +4x 3 +2x 2 +x in terms of [x]4,[x]3,[x]2 and [x].

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Here's the Solution to this Question

Given expression is-

3x^4+4x^3+2x^2+x


Let,

3x^4+4x^3+2x^2+x=3[x]^4+b[x^3]+c[x^2]+d[x]+0


\Rightarrow3x^4+4x^3+2x^2+x=3x(x-1)(x-2)(x-3)+bx(x-1)(x-2)+cx(x-1)+dx



Calculating the value of coefficient by putting x=1,2,3 and we get b=22,c=35,d=10


So The given polynomial can be represented as-

3[x]^4+22[x^3]+35[x^2]+10[x]

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