Final answer:
To solve (4x³ - 3x² + 5x + 6) / (x + 6) using synthetic division, follow a step-by-step process to find the quotient polynomial, which will be of degree 2.
Step-by-step explanation:
To find the quotient of (4x³ - 3x² + 5x + 6) / (x + 6) using synthetic division, we perform the following steps:
Write down the coefficients of the dividend (4, -3, 5, and 6).
Write the opposite number of the root of the divisor, in this case, -6 (since x + 6 = 0 when x = -6).
Bring down the leading coefficient (which is 4) to the bottom line.
Multiply this number by -6 and write the result under the next coefficient.
Add the numbers in this column and write the result underneath.
Continue this process until all coefficients have been used.
The numbers on the bottom line give the coefficients of the quotient polynomial.
The solution using synthetic division will yield a quotient polynomial of degree 2, since we started with a cubic polynomial and divided by a linear term.