Question:উৎপাদকে বিশ্লেষণ কর: `4x^4 + 12x^3 + 7x^2 - 3x - 2`
Answer ধরি, `f(x) = 4x^4 + 12x^3 + 7x^2 - 3x - 2` তাহলে, `f(- 1) = 4(- 1)^4 + 12 (- 1)^3 + 7 (- 1)^2 - 3(- 1) - 2` `= 4.1 + 12 (- 1) + 7.1 - 3 (- 1) - 2` = 4 - 12 + 7 + 3 - 2 = 14 - 14 = 0 :. {x - (- 1)} = (x + 1), f(x) এর একটি উৎপাদক। এখন, `x^4 + 12x^3 + 7x^2 - 3x - 2` `= 4x^4 + 4x^3 + 8x^3 + 8x^2 - x^2 - x - 2x - 2` `= 4x^3 (x + 1) + 8x^2 (x + 1) - x(x + 1) - 2(x + 1)` `= (x + 1) (4x^3 + 8x^2 - x - 2)` `= (x + 1) {4x^2 (x + 2) - 1(x + 2)}` `= (x + 1) (x + 2) (4x^2 - 1)` `= (x + 1) (x + 2) {(2x)^2 - 1^2}` `= (x + 1) (x + 2) (2x + 1) (2x - 1)` = (2x - 1) (x + 1) (x + 2) (2x + 1)` (Ans)
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utpadoke bisholeshn karo: `4x^4 + 12x^3 + 7x^2 - 3x - 2`