Divide. If there is a remainder,include it as (15x^3+9x+12)div 3x

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Divide. If there is a remainder,include it as (15x^3+9x+12)div 3x

Answer 1

To divide the polynomial \(15x^3 + 9x + 12\) by \(3x\), we can split the division into individual terms:\[\frac{15x^3}{3x} + \frac{9x}{3x} + \frac{12}{3x}\]Now, divide each term separately:\[\frac{15x^3}{3x} = 5x^2\]\[\frac{9x}{3x} = 3\]\[\frac{12}{3x} = 4x^{-1}\]However, since we are dividing polynomials, we typically do not include negative exponents in the quotient. Therefore, the term \(4x^{-1}\) represents the remainder. The correct division is:\[5x^2 + 3 + \frac{4}{3x}\]So, the quotient is \(5x^2 + 3\) with a remainder of \(4\), which can be written as:\[5x^2 + 3 + \frac{4}{3x}\]

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Divide. If there is a remainder,include it as (15x^3+9x+12)div 3x

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