Question:উৎপাদকে বিশ্লেষণ কর: `18x^3 + 15x^2 - x - 2`
Answer ধরি, `f(x) = 18x^3 + 15x^2 - x - 2` তাহলে, `f(- 1/2) = 18 (- 1/2)^3 + 15(- 1/2)^2 - (- 1/2) - 2` `= - 18 .1/2 + 15 . 1/4 + 1/2 - 2` `= (- 9 + 15 + 2 - 8)/4` `= (17 - 17)/4 = 0/4 = 0` `:. {x - (- 1/2)} = (x + 1/2)` অর্থাৎ (2x + 1), f(x) এর একটি উৎপাদক। এখন, `18x^3 + 15x^2 - x - 2` `= 18x^3 + 9x^2 + 6x^2 + 3x - 4x - 2` `= 9x^2 (2x + 1) + 3x (2x + 1) - 2(2x + 1)` `= (2x + 1) (9x^2 + 3x - 2)` `= (2x + 1) (9x^2 + 6x - 3x - 2)` `= (2x + 1) {3x (3x + 2) - 1(3x + 2)}` `= (2x + 1) (3x + 2) (3x - 1)` (Ans)
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utpadoke bisholeshn karo: `18x^3 + 15x^2 - x - 2`