Question:উৎপাদকে বিশ্লেষণ কর: `x^3 + 4x^2 + x - 6`
Answer ধরি, `f(x) = x^3 + 4x^2 + x - 6` তাহলে, `f(1) = (1)^3 + 4(1)^2 + 1 - 6` `= 1 + 4.1 + 1 - 6` = 6 - 6 = 0 :. (x - 1), f(x) এর একটি উৎপাদক। এখন, `x^3 + 4x^2 + x - 6` `= x^3 - x^2 + 5x^2 - 5x + 6x - 6` `= x^2 (x - 1) + 5x (x - 1) + 6 (x - 1)` `= (x - 1) (x^2 + 5x + 6)` `= (x - 1) (x^2 + 3x + 2x + 6)` `= (x - 1) {x (x + 3) + 2(x + 3)}` `= (x - 1) (x + 3) (x + 2)` `= (x - 1) (x + 2) (x + 3)` (Ans)
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utpadoke bisholeshn karo: `x^3 + 4x^2 + x - 6`