Answer to Question #236765 in Calculus for CCW

Question #236765

Synthetic Division:

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

(show step by step)


1
Expert's answer
2021-09-17T04:08:47-0400

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)}



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