Question

without actual division prove that 2x^-6x^+3x^+3x-2 is exactly divisible byx^-3x+2​

Answer 1

x²-3x+2 can be factorised as (x-2)(x-1).

Let

$f(x)= 2x^4-6x^3+3x^2+3x-2\\</p><p>\mathrm{Thus, }\\</p><p>f(1)=0; \\</p><p>f(2)=0.\\</p><p>\mathrm {Hence \: by\: \textcolor{red}{factor \: theorem}, it \: is \: a \: divisor.}$