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Synthetic division

Synthetic division is a simplified method of dividing a polynomial p(x) by x-r, where r is any assigned number.

Divide P(x)=2x3 + x2 - 3x + 5 by Q(x)=x-1 using synthetic division

1.Write the terms of the dividend in descending powers of the variable and fill in missing terms using zero for coefficients. Write the constant term r from the divisor on the left. Bring down the first term in the divisor to the third row, leaving a blank row for now, as you can see at (1)

2. Multiply the term in the quotient row 2 by the divisor and write the product in the second row, under the second term in the first row. (2)

3. Add the numbers in the column formed, and write the sum as the second term in the quotient row. Continue this process until all of the terms in the top row have a number under them (3) (4).

4. The third row is the quotient row with the last term (red) being the remainder
Remainder = 5 C(x)=2x2 + 3x
Then: 2x3 + x2 - 3x + 5 =(x-1) (2x2 + 3x) +5

Use synthetic division to divide x3-13x-12 by x+1:

Quotient: x2-x-12 Remainder: 0

Divide using the synthetic division.
$P(x)=-5x^4+7x^3-3x-8$ by Q(x)=$x-1$

 Solution: Quotient: x3 x2 x Remainder: