Question

8 b) Express 3x

4 +4x

3 +2x

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

Answer 1

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-

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