Questions: Find the quotient using long division. 3x^3 + 2x^2 - 19x + 1 divided by x - 2

Transcript text: Find the quotient using long division. \[ \frac{3 x^{3}+2 x^{2}-19 x+1}{x-2} \]

Solution

Step 1: Divide the Leading Terms

Divide $3 x^{3}$ by $x$ , resulting in $3 x^{2}$ . The remaining polynomial is $8 x^{2} - 19 x + 1$ .

Step 2: Continue Division

Divide $8 x^{2}$ by $x$ , resulting in $8 x$ . The remaining polynomial is $1 - 3 x$ .

Step 3: Final Division

Divide $-3 x$ by $x$ , resulting in $-3$ . The remaining polynomial is $-5$ .

Step 4: Write the Quotient and Remainder

The quotient is $3 x^{2} + 8 x - 3$ and the remainder is $-5$ .

Step 5: Express the Final Result

The complete division expression is given by: $\frac{3 x^{3} + 2 x^{2} - 19 x + 1}{x - 2} = 3 x^{2} + 8 x - 3 - \frac{5}{x - 2}$

$\boxed{3x^{2} + 8x - 3 - \frac{5}{x - 2}}$

Was this solution helpful?

Unhelpful

Helpful