How do you find the quotient of #(n^2+3n+10)div(n-1)# using long division?

Answer 1

#n-4# and remainder of# 6/(n-1)#

#color(white)(..........)color(white)(............)n-4# #n-1|overline(n^2+3n+10)# #color(white)(............)ul(n^2-n)# #color(white)(......................)4n+10# #color(white)(......................)ul(4n+04)# #color(white)(..................................)6#
#(n^2+3n+10) / (n-1) = n-4+6/(n-1)#
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Answer 2

To find the quotient of (n^2+3n+10) divided by (n-1) using long division, follow these steps:

  1. Begin by dividing the first term of the numerator (n^2) by the first term of the denominator (n). The result is n.

  2. Multiply the entire denominator (n-1) by the quotient obtained in step 1 (n). This gives you n(n-1), which is n^2-n.

  3. Subtract the result obtained in step 2 from the numerator (n^2+3n+10). This gives you a new polynomial: 3n+10.

  4. Bring down the next term from the numerator, which is 3n.

  5. Divide the first term of the new polynomial (3n) by the first term of the denominator (n). The result is 3.

  6. Multiply the entire denominator (n-1) by the quotient obtained in step 5 (3). This gives you 3(n-1), which is 3n-3.

  7. Subtract the result obtained in step 6 from the new polynomial (3n+10). This gives you a new polynomial: 13.

  8. Bring down the next term from the numerator, which is 10.

  9. Divide the first term of the new polynomial (13) by the first term of the denominator (n). The result is 13/n.

  10. Multiply the entire denominator (n-1) by the quotient obtained in step 9 (13/n). This gives you 13(n-1), which is 13n-13.

  11. Subtract the result obtained in step 10 from the new polynomial (13). This gives you a remainder of 13.

Therefore, the quotient of (n^2+3n+10) divided by (n-1) using long division is n+3 with a remainder of 13.

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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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