Final answer:
To divide z³ + 7z + 10 by z - 6 using long division, start by dividing the first term of the numerator by the first term of the denominator. Next, subtract the result from the numerator and continue dividing until the remainder is zero or of a lower degree than the denominator.
Step-by-step explanation:
To divide z³ + 7z + 10 by z - 6 using long division, we start by dividing the first term of the numerator by the first term of the denominator. Therefore, z³ ÷ z = z². Next, we multiply the entire denominator (z - 6) by the result we obtained (z²), which gives us z²(z - 6) = z³ - 6z².
Subtracting z³ - 6z² from the original numerator, we get 7z + 10 - (z³ - 6z²) = 7z + 10 - z³ + 6z².
Now we continue dividing the new numerator (7z + 10 - z³ + 6z²) by the denominator (z - 6). The process is repeated until we reach a remainder of zero or a degree lower than the denominator.