Write the coefficients of 2x3 + 11x2 + 2x − 15 in Row 1 of the Array below. (If a power of x is ever "skipped" in a dividend, a zero is written to mark its place in the Array.)
The divisor in this case is x − 5, and already in the form "x − a", so a = 5. (Note that for x + 5, the divisor would be written as "x − -5" and "a" would equal -5.) Write an underlined 5 to the right of -15 in Row 1 of the Array.
Place a 0 in Row 2 of Column 1 and add 2 + 0 to place a sum of 2 in Row 3 of Column 1. Next, multiply this sum of 2 by the underlined 5 to obtain 10 which is placed in Row 2 of Column 2. Then sum 11 and 10 to yield 21 which is placed in Row 3 of Column 2.
The product of 5 and 21 or 105 is then placed in Row 2 of Column 3 and a sum of (105 + 2) or 107 is placed in Row 3 of Column 3. To complete the Array, the product of 5 and 107 or 535 is placed in Row 2 of Column 4 under -15 and the sum of -15 and 535 or 520 is placed in Row 3 of Column 4.
The highest power of x in the dividend is x3, so the highest power of x in the quotient will be x(3 − 1) or x2.
C1 C2 C3 C4
R1 2 11 2 -15 5
R2 0 10 105 535
R3 2 21 107 520
Using the coefficients shown in Row 3, the quotient is then written as 2x2 + 21x + 107 with a remainder of 520 or 2x2 + 21x + 107 + 520/(x − 5) where x ≠ 5.
