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

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There are four possible roots, I need to know how to sythen.
asked Mar 12, 2014 in ALGEBRA 2 by skylar Apprentice

1 Answer

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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.

image

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

image

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

image

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

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

image

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

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

image

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

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

image.

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 image.

answered Apr 19, 2014 by steve Scholar
edited Apr 19, 2014 by steve

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