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$x^3 + 4x^2 + 5x + 6$ divide by $x + 6$

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Multiply and divide rational expressions

Full solution

Q.

x^3 + 4x^2 + 5x + 6

divide by

x + 6

Set up the division: We're gonna do polynomial long division, just like dividing numbers. Set up the division.
Divide $x^3$ : Divide $x^3$ by $x$ to get $x^2$ . Multiply $x^2$ by $x + 6$ to get $x^3 + 6x^2$ . Subtract this from the original polynomial.
Subtract and continue: After subtracting, we get $-2x^2 + 5x$ . Now, divide $-2x^2$ by $x$ to get $-2x$ . Multiply $-2x$ by $x + 6$ to get $-2x^2 - 12x$ .
Divide $-2x^2$ : Subtract $-2x^2 - 12x$ from $-2x^2 + 5x$ to get $17x$ . Divide $17x$ by $x$ to get $17$ . Multiply $17$ by $x + 6$ to get $17x + 102$ .
Subtract and correct: Subtract $17x + 102$ from $17x + 6$ . Oops, we made a mistake here, it should be subtracting from $17x + 6$ , not adding.

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