Answer:
The error is -12x² - 14x = - 26x² because 12x² and 14x are unlike terms, so we can not add them
To prevent it the dividend must be written as 6x³ + 0x² - 14x + 1
Explanation:
In the division, you must arrange the dividend according to the greatest power of the variable, and put 0 as a coefficient of the missing term to avoid adding, unlike terms.
Example:
If the dividend is 3x³ - 2x + 5, then you must write it as 3x³ + 0x² - 2x + 5
Let us solve our question
∵ The dividend is 6x³ + 1 - 14x
→ You must arrange it from the greatest power of x
∴ The dividend is 6x³ - 14x + 1
∵ The term of x² is missing
→ Write it in the dividend with a coefficient of 0
∴ The dividend is 6x³ + 0x² - 14x + 1
The error is the adding of unlike terms
∵ 6x³ - 14x + 1 ÷ 3x + 6 = 2x² and [6x³ - 14x + 1 - 6x³ - (6x³ + 12x²)]
∵ [6x³ - 14x + 1 - 6x³ - (6x³ + 12x²)] = 6x³ - 14x + 1 - 6x³ - 12x²
∵ 6x³ - 14x + 1 - 6x³ - 12x² = 0 - 12x² - 14x + 1
∵ 0 - 12x² - 14x + 1 = -26x² + 1 ⇒ error
∴ The error is -12x² - 14x = - 26x² because 12x² and 14x are unlike terms,
so we can not add them
→ To prevent it, write 0 as a coefficient of the missing term
∵ The missing term is the term of x²
∴ Add to the dividend the term 0x²
∴ The dividend must be written as 6x³ + 0x² - 14x + 1