Question 2.4.4: Using Synthetic Division Use synthetic division to divide 5x...
Using Synthetic Division
Use synthetic division to divide 5x³ + 6x + 8 by x + 2.
The divisor must be in the form x – c. Thus, we write x + 2 as x – (-2). This means that c = -2. Writing a 0 coefficient for the missing x²-term in the dividend, we can express the division as follows:
x-(-2))\overline{5x^3 + 0x^2 + 6x + 8.}
Now we are ready to set up the problem so that we can use synthetic division.
We begin the synthetic division process by bringing down 5. This is followed by a series of multiplications and additions.
The numbers in the last row represent the coefficients of the quotient and the remainder. The degree of the first term of the quotient is one less than that of the dividend. Because the degree of the dividend, 5x³ + 6x + 8, is 3, the degree of the quotient is 2. This means that the 5 in the last row represents 5x².
Thus,
