Answer:
-14x and 12x² are not like terms, so they can’t be subtracted.
To prevent this error, be sure to line up like terms.
Step-by-step explanation:
The long division method is one of the several ways to divide polynomials. The error in the work is in the subtraction of [tex]6x^3 + 12x^2[/tex] from [tex]6x^3 - 14x + 1[/tex]
From the long division (see attachment);
[tex]6x^3 + 12x^2[/tex] was subtracted from [tex]6x^3 - 14x + 1[/tex] to give [tex]-26x^2 + 1[/tex]
For proper representation, we have:
[tex]6x^3 - 14x + 1 - (6x^3 + 12x^2) = -26x^2 + 1[/tex]
This subtraction is wrong, and the proof is as follows:
[tex]6x^3 - 14x + 1 - (6x^3 + 12x^2) = -26x^2 + 1[/tex]
Open bracket
[tex]6x^3 - 14x + 1 - 6x^3 - 12x^2 = -26x^2 + 1[/tex]
Collect like terms
[tex]6x^3 - 6x^3 - 12x^2 - 14x + 1 = -26x^2 + 1[/tex]
[tex]- 12x^2 - 14x + 1 = -26x^2 + 1[/tex]
Because [tex]- 12x^2[/tex] and [tex]- 14x[/tex] are not like terms, the end result of the subtraction will be:[tex]- 12x^2 - 14x + 1[/tex] and not [tex]-26x^2 + 1[/tex]
i.e.
[tex]6x^3 - 14x + 1 - (6x^3 + 12x^2) \ne -26x^2 + 1[/tex]
[tex]6x^3 - 14x + 1 - (6x^3 + 12x^2) =- 12x^2 - 14x + 1[/tex]
Hence, there is an error in the long division, and the error is in the subtraction of [tex]6x^3 + 12x^2[/tex] from [tex]6x^3 - 14x + 1[/tex]
Read more about polynomial long divisions at:
https://brainly.com/question/12562913
