Divide Using Synthetic Division (6+a^3-a)÷(a+2)

Problem

(a3−a+6)÷(a+2)

Solution

1. Rewrite the dividend in descending order of powers and include a placeholder for the missing a2 term.

a3+0*a2−a+6

2. Identify the divisor constant k from the form (a−k) Since the divisor is (a+2) then k=−2

3. Set up the synthetic division by listing the coefficients of the dividend: 1 0 −1 and 6

−2∣1*0−1*6

4. Bring down the first coefficient (1 to the bottom row.

−2∣1*0−1*6

↓

1

5. Multiply the divisor k=−2 by the value in the bottom row (1 and place the result (−2 under the next coefficient (0.

−2×1=−2

6. Add the column values (0 + (-2) = -2$) and place the result in the bottom row.

−2∣1*0−1*6

−2

_*_*_*_*_*_*_*_*_*_*_*_*_*_*_*_*_*_*_*_

1−2

7. Repeat the multiply-and-add process for the remaining columns.

−2×−2=4

−1+4=3

−2×3=−6

6+(−6)=0

8. Interpret the bottom row (1,−2,3,0) as the coefficients of the quotient and the remainder. The quotient starts one degree lower than the dividend (a2.

1*a2−2*a+3

Remainder=0

Final Answer

(a3−a+6)÷(a+2)=a2−2*a+3

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