QuestionSeptember 19, 2025

3 x + 2 longdiv ( 9 x ^ ( 3 ) + 2 7 x ^ ( 2 ) + 1 7 x + 2 )

3 x + 2 longdiv ( 9 x ^ ( 3 ) + 2 7 x ^ ( 2 ) + 1 7 x + 2 )
3 x + 2 longdiv ( 9 x ^ ( 3 ) + 2 7 x ^ ( 2 ) + 1 7 x + 2 )

Solution
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Answer

3x^2 + 7x + 1 Explanation 1. Set up polynomial long division Divide first term: \frac{9x^3}{3x} = 3x^2. Multiply (3x+2)(3x^2) = 9x^3 + 6x^2. Subtract from dividend: (9x^3+27x^2+17x+2) - (9x^3+6x^2) = 21x^2 + 17x + 2. 2. Second term of quotient Divide 21x^2 by 3x: \frac{21x^2}{3x} = 7x. Multiply (3x+2)(7x) = 21x^2 + 14x. Subtract: (21x^2+17x+2) - (21x^2+14x) = 3x + 2. 3. Final term of quotient Divide 3x by 3x: \frac{3x}{3x} = 1. Multiply (3x+2)(1) = 3x + 2. Subtract: (3x+2) - (3x+2) = 0.

Explanation

1. Set up polynomial long division <br /> Divide first term: $\frac{9x^3}{3x} = 3x^2$. <br />Multiply $(3x+2)(3x^2) = 9x^3 + 6x^2$. Subtract from dividend: $(9x^3+27x^2+17x+2) - (9x^3+6x^2) = 21x^2 + 17x + 2$. <br /><br />2. Second term of quotient <br /> Divide $21x^2$ by $3x$: $\frac{21x^2}{3x} = 7x$. <br />Multiply $(3x+2)(7x) = 21x^2 + 14x$. Subtract: $(21x^2+17x+2) - (21x^2+14x) = 3x + 2$. <br /><br />3. Final term of quotient <br /> Divide $3x$ by $3x$: $\frac{3x}{3x} = 1$. <br />Multiply $(3x+2)(1) = 3x + 2$. Subtract: $(3x+2) - (3x+2) = 0$.
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