Explain the error in the work and how you might prevent it

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

Step-by-step 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

w'x is 0.

hope it