Question

Study the partial work shown for the following division problem.

Divide 6x3 + 1 − 14x by 3x + 6.

3 x + 6 StartLongDivisionSymbol 6 x cubed minus 14 x + 1 EndLongDivision Symbol. minus 6 x cubed + 12 x squared to get a remainder of negative 26 x squared + 1 and a quotient of 2 x squared.
Do you see any error in the work so far?

Answer 1

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:

Answer 2

The long division method is one of the several ways to divide polynomials. The error in the work is in the subtraction of $6x^3 + 12x^2$ from $6x^3 - 14x + 1$

From the long division (see attachment);

$6x^3 + 12x^2$ was subtracted from $6x^3 - 14x + 1$ to give $-26x^2 + 1$

For proper representation, we have:

$6x^3 - 14x + 1 - (6x^3 + 12x^2) = -26x^2 + 1$

This subtraction is wrong, and the proof is as follows:

$6x^3 - 14x + 1 - (6x^3 + 12x^2) = -26x^2 + 1$

Open bracket

$6x^3 - 14x + 1 - 6x^3 - 12x^2 = -26x^2 + 1$

Collect like terms

$6x^3 - 6x^3 - 12x^2 - 14x + 1 = -26x^2 + 1$

$- 12x^2 - 14x + 1 = -26x^2 + 1$

Because $- 12x^2$ and $- 14x$ are not like terms, the end result of the subtraction will be:$- 12x^2 - 14x + 1$ and not $-26x^2 + 1$

i.e.

$6x^3 - 14x + 1 - (6x^3 + 12x^2) \ne -26x^2 + 1$

$6x^3 - 14x + 1 - (6x^3 + 12x^2) =- 12x^2 - 14x + 1$

Hence, there is an error in the long division, and the error is in the subtraction of $6x^3 + 12x^2$ from $6x^3 - 14x + 1$

Read more about polynomial long divisions at:

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