Question:উৎপাদকে বিশ্লেষণ কর: `x^6 - x^5 + x^4 - x^3 + x^2 - x`
Answer `x^6 - x^5 + x^4 - x^3 + x^2 - x` `= x (x^5 - x^4 + x^3 - x^2 + x - 1)` এখন, মনে করি, f(x) `= x^5 - x^4 + x^3 - x^2 + x - 1` :. f(1) `= (1)^5 - (1)^4 + (1)^3 - (1)^2 + (1) - 1` `= 1 - 1 + 1 - 1 + 1 - 1` = 3 - 3 = 0 :. (x - 1), f (x) এর একটি উৎপাদক। এখন, `x^5 - x^4 + x^3 - x^2 + x - 1` `= x^4 (x - 1) + x^2(x - 1) + 1(x - 1)` `= (x - 1) (x^4 + x^2 + 1)` `= (x - 1) {(x^2)^2 + 2.x^2.1 + (1)^2 - x^2}` `= (x - 1) {(x^2 + 1)^2 - (x)^2}` `= (x - 1) (x^2 + 1 + x) (x^2 + 1 - x)` `= (x - 1) (x^2 + x + 1) (x^2 - x + 1)` `:. x^6 - x^5 + x^4 - x^3 + x^2 - x ` `= x(x - 1) (x^2 + x + 1) (x^2 - x + 1)` (Ans)
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