Answer to Question #236765 in Calculus for CCW

Question

Synthetic Division:

1. (2.) (3x^2 - 4x + 3) / (2x - 1)

(show step by step)

Answer 1

STEP 1: The leading coefficient of the divisor should equal 1, so divide all coefficients of both the dividend and divisor by 2.

$3x^2 -4x+3 \text{ becomes } \frac{3}{2}x -2x + \frac{3}{2} \\ 2x-1 \text{ becomes } x-\frac{1}{2}.$

STEP 2: Write the polynomial being divided in descending order. Then, write only it's coefficient and constant, using 0 for any missing terms.

$\frac{3}{2}x -2x + \frac{3}{2}\\\\ \frac{3}{2}~~~-2~~~~~~~\frac{3}{2}$

STEP 3: Write the constant, a, of the divisor $x-a$ , to the left. $a=\frac{1}{2}$

$\frac{1}{2}~|~\frac{3}{2}~~~-2~~~~~~~\frac{3}{2}$

STEP 4: Bring down the first coefficient as shown below

STEP 5: Multiply the first coefficients by the divisor. Then write this product under the second coefficient. Add the second coefficient with the product and write the sum as shown below

STEP 6: Continue this process of multiplying and adding until there is a sum for the last column.

The number along the bottom row are the coefficient of the quotient with powers of x in descending order. The last coefficient is the remainder. The first power is 1 less than the highest power of the polynomial that was been divided.

The division answer is;

$\frac{3}{2}x -\frac{5}{4}+\frac{\frac{7}{8}}{x-\frac{1}{2}}= \frac{3}{2}x -\frac{5}{4}+\frac{7}{4(2x-1)}$