Questions: Find the quotient and remainder using long division. (x^3 + 3x^2 - 18) / (x - 2) The quotient is The remainder is

Transcript text: Question 6 Find the quotient and remainder using long division. \[ \frac{x^{3}+3 x^{2}-18}{x-2} \] The quotient is $\square$ The remainder is $\square$ Question Help: Video Submit Question

Solution

Solution Steps

Step 1: Setup

Given the dividend polynomial $P(x) = x^3 + 3x^2 - 18$ and the divisor polynomial $D(x) = x - 2$.

Step 2: Division

Divide the leading term of the current remainder by the leading term of $D(x)$ to find the next term of $Q(x)$: $1.0x^2$.

Step 3: Multiply and Subtract

Multiply $D(x)$ by $1.0x^2$ and subtract from the current remainder to get the new remainder $R(x) = 5.0x^2 - 18$.

Step 3: Division

Divide the leading term of the current remainder by the leading term of $D(x)$ to find the next term of $Q(x)$: $5.0x^1$.

Step 4: Multiply and Subtract

Multiply $D(x)$ by $5.0x^1$ and subtract from the current remainder to get the new remainder $R(x) = 10.0x - 18$.

Step 4: Division

Divide the leading term of the current remainder by the leading term of $D(x)$ to find the next term of $Q(x)$: $10.0x^0$.

Step 5: Multiply and Subtract

Multiply $D(x)$ by $10.0x^0$ and subtract from the current remainder to get the new remainder $R(x) = 2$.

Final Answer:

The quotient $Q(x) = 1.0x^2 + 5.0x + 10$ and the remainder $R(x) = 2$ after dividing $P(x)$ by $D(x)$.

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