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How do you long divide # x^3 - 7x - 6 div x+1 #?

Answer 1

by Ruffini rule

Ruffini scheme:
first row I get coefficients,
second row on the left the known term with changed sign (-1) and
I get results of sums in columns and products by -1
third row: I get result's coefficients

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Answer 2

Christian Antunez

To long divide ( x^3 - 7x - 6 ) by ( x+1 ), follow these steps:

Divide the first term of the dividend (( x^3 )) by the first term of the divisor (( x )), which gives ( x^2 ). Write this as the first term of the quotient.
Multiply the entire divisor (( x+1 )) by ( x^2 ) and write the result below the dividend.
Subtract the result obtained in step 2 from the dividend (( x^3 - x^3 - x^2 )). This leaves ( -x^2 - 7x - 6 ).
Bring down the next term from the dividend, which is ( -7x ).
Repeat steps 1-3 using the result obtained from step 4 as the new dividend (( -x^2 - 7x )).
Continue this process until all terms in the dividend have been used.
The final result will be the quotient (( x^2 - 8x + 1 )) and the remainder (0).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.