# How do you find the quotient of #(r^2-12r+11)div(r-1)#?

See a solution process below:

We can rewrite this expression as:

We can factor the numerator as:

We can now cancel common terms in the numerator and denominator to give:

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To find the quotient of (r^2-12r+11) divided by (r-1), you can use long division or synthetic division.

Using long division:

- Divide the first term of the dividend (r^2) by the divisor (r), which gives r as the first term of the quotient.
- Multiply the divisor (r-1) by the first term of the quotient (r), which gives r^2-r.
- Subtract this result (r^2-r) from the dividend (r^2-12r+11), which gives -11r+11.
- Bring down the next term (-11r) and repeat the process.
- Divide (-11r) by (r), which gives -11 as the next term of the quotient.
- Multiply the divisor (r-1) by the new term of the quotient (-11), which gives -11r+11.
- Subtract this result (-11r+11) from the remaining terms (-11r+11), which gives 0.
- There is no remainder, so the quotient is r-11.

Using synthetic division:

- Write the coefficients of the dividend (r^2-12r+11) in descending order: 1, -12, 11.
- Write the constant term of the divisor (r-1) as the divisor: 1.
- Bring down the first coefficient (1) and perform the division: 1 divided by 1 is 1.
- Multiply the divisor (1) by the result (1), which gives 1.
- Subtract this result (1) from the next coefficient (-12), which gives -13.
- Multiply the divisor (1) by the new result (-13), which gives -13.
- Subtract this result (-13) from the last coefficient (11), which gives -2.
- The resulting coefficients are 1 and -13, which represent the quotient coefficients.
- Therefore, the quotient is r-11.

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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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