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(v^(3)+4v^(2)-15 v+42)÷(v+7)

$2$ ) $\left(v^{3}+4 v^{2}-15 v+42\right) \div(v+7)$

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Divide polynomials using long division

Full solution

Q.

2

)

\left(v^{3}+4 v^{2}-15 v+42\right) \div(v+7)

Set up long division: First, let's set up the long division of the polynomials. $\newline$ We're dividing $(v^{3}+4v^{2}-15v+42)$ by $(v+7)$ .
Divide first term: Divide the first term of the dividend, $v^3$ , by the first term of the divisor, $v$ , to get $v^2$ . Write $v^2$ above the division bar.
Subtract and bring down: Multiply $v^2$ by $(v+7)$ to get $v^3+7v^2$ . Subtract this from the first two terms of the dividend.
Divide next term: After subtracting, we bring down the next term of the dividend, which is $-15v$ . $\newline$ Now we have $-3v^2-15v$ .
Subtract and bring down: Divide $-3v^2$ by $v$ to get $-3v$ . Write $-3v$ above the division bar next to $v^2$ .
Divide last term: Multiply $-3v$ by $(v+7)$ to get $-3v^2-21v$ . $\newline$ Subtract this from $-3v^2-15v$ .
Subtract and finish: After subtracting, we get $6v$ . Bring down the last term of the dividend, which is $+42$ . Now we have $6v+42$ .
Subtract and finish: After subtracting, we get $6v$ . Bring down the last term of the dividend, which is $+42$ . Now we have $6v+42$ . Divide $6v$ by $v$ to get $6$ . Write $6$ above the division bar next to $-3v$ .
Subtract and finish: After subtracting, we get $6v$ . Bring down the last term of the dividend, which is $+42$ . Now we have $6v+42$ . Divide $6v$ by $v$ to get $6$ . Write $6$ above the division bar next to $-3v$ . Multiply $6$ by $(v+7)$ to get $6v+42$ . Subtract this from $6v+42$ .
Subtract and finish: After subtracting, we get $6v$ . Bring down the last term of the dividend, which is $+42$ . Now we have $6v+42$ . Divide $6v$ by $v$ to get $6$ . Write $6$ above the division bar next to $-3v$ . Multiply $6$ by $(v+7)$ to get $6v+42$ . Subtract this from $6v+42$ . After subtracting, we get $+42$ $2$ . There's no remainder, so we've finished the division.

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