How to divide synthetically x^4-8x^3+26x^2-40x+21=0 by 2-i square root 3

Question

There are four possible roots, I need to know how to sythen.

Answer 1

The function is , and the root is .

Use synthetic division to find .

Step 1 : Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients as shown at the right.

Step 2 : Write the constant r of the divisor (x - r) to the left. In this case, . Bring the first coefficient, 1, down.

Step 3 : Multiply the first coefficient by r : . Write the product under the second coefficient, - 8 and add : .

Step 4 : Multiply the sum, , by r : .

Write the product under the next coefficient, 26 and add : .

Step 5 : Multiply the sum, , by r : .

Write the product under the next coefficient, - 40 and add : .

Step 6 : Multiply the sum, , by r : .

Write the product under the next coefficient, 21 and add : - 21 + 21 = 0. The remainder is 0.

.

The numbers along the bottom row are the coefficients of the quotient. Start with the power of x that is one less than the degree of the dividend. Thus, the quotient is .