To put the polynomial \(3x^3(x-1) + x(x-1)\) in standard form, we can simplify each term first.
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Distributing \(3x^3(x-1)\): \[ 3x^3(x - 1) = 3x^4 - 3x^3 \]
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Distributing \(x(x-1)\): \[ x(x - 1) = x^2 - x \]
Now we add these two results together: \[ 3x^4 - 3x^3 + x^2 - x \]
Next, we can organize it in standard form, which is typically written in descending order of degrees: \[ 3x^4 - 3x^3 + x^2 - x \]
Thus, the polynomial in standard form is: \[ 3x^4 - 3x^3 + x^2 - x \]
The correct response is: 3x⁴ − 3x³ + x² − x