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(x^(3)-2x^(2)-3)xx(-x)...

`(x^(3)-2x^(2)-3)xx(-x)`

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To solve the expression \((x^3 - 2x^2 - 3)(-x)\), we will follow these steps: ### Step 1: Distribute \(-x\) to each term in the polynomial We will multiply \(-x\) by each term in the polynomial \(x^3 - 2x^2 - 3\). \[ -x \cdot x^3, \quad -x \cdot (-2x^2), \quad -x \cdot (-3) \] ### Step 2: Perform the multiplication Now we will calculate each multiplication: 1. \(-x \cdot x^3 = -x^{3+1} = -x^4\) 2. \(-x \cdot (-2x^2) = 2x^{2+1} = 2x^3\) (Note: Negative times negative gives a positive) 3. \(-x \cdot (-3) = 3x\) (Again, negative times negative gives a positive) ### Step 3: Combine the results Now we combine all the terms we calculated: \[ -x^4 + 2x^3 + 3x \] ### Final Result Thus, the final expression after multiplying \((x^3 - 2x^2 - 3)\) by \(-x\) is: \[ -x^4 + 2x^3 + 3x \] ---
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Knowledge Check

  • If x ne -1, 2 and 5, then the simplified value of {(2(x^(3) - 8))/(x^(2)-x-2) xx (x^(2) + 2x + 1)/(x^(2) - 4x - 5) div (x^(2) + 2x+4)/(3x-15)} is equal to :

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