Question

Synthetic Division:

1. (2x^4 + 7x^3 + x - 12) / (x+ 3)

(show step by step)

Answer 1

STEP 1: Write the polynomial being divided in descending order. Then, write only it's coefficient and constant, using 0 for any missing terms.

$2x^4 + 7x^3 + 0x^2 + x- 12\\ 2~~~~~~~~~7~~~~~~~~~0~~~~~~~~~1~~-12$

STEP 2: Write the constant, a, of the divisor $x-a$ , to the left. $a=-3.$

$-3|2~~~~~~~~~7~~~~~~~~~0~~~~~~~~~1~~-12$

STEP 3: Bring down the first coefficient as shown below.

STEP 4: Multiply the first coefficients by the device or, - 3. Then write this product under the second coefficient. Add the second coefficient with the products and write the sum as shown below

STEP 5: 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;

$2x^3+x^2-3x+10-\frac{42}{x+3}.$