Question

use the long division method to find the result when $6x^3 + 26x^2 + 23x + 5$ is divided by $3x + 1$.

Explanation:

Step1: Divide leading terms

$\frac{6x^3}{3x} = 2x^2$

Step2: Multiply divisor by $2x^2$

$2x^2(3x + 1) = 6x^3 + 2x^2$

Step3: Subtract from dividend

$(6x^3 + 26x^2 + 23x + 5) - (6x^3 + 2x^2) = 24x^2 + 23x + 5$

Step4: Divide new leading terms

$\frac{24x^2}{3x} = 8x$

Step5: Multiply divisor by $8x$

$8x(3x + 1) = 24x^2 + 8x$

Step6: Subtract from new dividend

$(24x^2 + 23x + 5) - (24x^2 + 8x) = 15x + 5$

Step7: Divide leading terms again

$\frac{15x}{3x} = 5$

Step8: Multiply divisor by 5

$5(3x + 1) = 15x + 5$

Step9: Subtract to find remainder

$(15x + 5) - (15x + 5) = 0$

Answer:

$2x^2 + 8x + 5$