How do you divide #(x^3 - 7x - 6)/(x+1)#?

Answer 1

Quotient is #x^2-x-6# and remainder is #0#

#x^3-7x-6#
=#x^3+x^2-x^2-x-6x-6#
=#x^2*(x+1)-x*(x+1)-6*(x+1)#
=#(x^2-x-6)*(x+1)#
Hence quotient is #x^2-x-6# and remainder is #0#
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Answer 2

To divide (x^3 - 7x - 6) by (x+1), you can use long division. Here are the steps:

  1. Divide the first term of the numerator (x^3) by the first term of the denominator (x). This gives x^2.
  2. Multiply the entire denominator (x+1) by the quotient obtained in step 1 (x^2). This gives x^3 + x^2.
  3. Subtract the result obtained in step 2 from the numerator (x^3 - 7x - 6). This gives -8x^2 - 7x - 6.
  4. Bring down the next term from the numerator (-8x^2) and repeat steps 1-3.
  5. Divide the first term of the new numerator (-8x^2) by the first term of the denominator (x). This gives -8x.
  6. Multiply the entire denominator (x+1) by the quotient obtained in step 5 (-8x). This gives -8x^2 - 8x.
  7. Subtract the result obtained in step 6 from the new numerator (-8x^2 - 7x - 6). This gives x - 6.
  8. Bring down the next term from the numerator (x) and repeat steps 1-3.
  9. Divide the first term of the new numerator (x) by the first term of the denominator (x). This gives 1.
  10. Multiply the entire denominator (x+1) by the quotient obtained in step 9 (1). This gives x + 1.
  11. Subtract the result obtained in step 10 from the new numerator (x - 6). This gives -7.
  12. There are no more terms left in the numerator, so the division is complete.
  13. The quotient is x^2 - 8x + 1, and the remainder is -7.
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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.

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.

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.

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.

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