# How do you divide #(8r^3 + 27s^3) /( 4r^2 - 6rs + 9s^2)#?

But the latter factor is just the denominator.

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To divide (8r^3 + 27s^3) by (4r^2 - 6rs + 9s^2), you can use polynomial long division or synthetic division. Here, I'll demonstrate polynomial long division:

- Divide the first term of the numerator by the first term of the denominator. This gives you the first term of the quotient.
- Multiply the entire denominator by the first term of the quotient, and subtract this product from the numerator.
- Bring down the next term from the numerator.
- Repeat steps 1-3 until you have no more terms in the numerator or the degree of the remaining term in the numerator is less than the degree of the denominator.

Given: Numerator: 8r^3 + 27s^3 Denominator: 4r^2 - 6rs + 9s^2

Step 1: First term of the quotient: (8r^3) / (4r^2) = 2r

Step 2: 2r * (4r^2 - 6rs + 9s^2) = 8r^3 - 12r^2s + 18rs^2 Subtract this from the numerator: (8r^3 + 27s^3) - (8r^3 - 12r^2s + 18rs^2) = 27s^3 + 12r^2s - 18rs^2

Step 3: Bring down the next term from the numerator: 27s^3

Step 4: Repeat steps 1-3:

Step 1: (27s^3) / (4r^2) = 0 (because the degree of 27s^3 is less than the degree of 4r^2)

Step 2: 0 * (4r^2 - 6rs + 9s^2) = 0 Subtract this from the remaining term in the numerator: 27s^3 - 0 = 27s^3

Since there are no more terms in the numerator, the division is complete.

The quotient is 2r, and there is a remainder of 27s^3. Therefore, the division result is:

Quotient: 2r Remainder: 27s^3

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To divide (\frac{{8r^3 + 27s^3}}{{4r^2 - 6rs + 9s^2}}), you can use polynomial long division or synthetic division. Here, I'll demonstrate polynomial long division:

- Divide the first term of the numerator by the first term of the denominator. This gives you the first term of the quotient.
- Multiply the entire denominator by this first term of the quotient.
- Subtract the result from the numerator.
- Bring down the next term from the numerator and repeat steps 1-3 until you've divided all terms.

Here's the process step by step:

- Divide (8r^3) by (4r^2), which gives (2r).
- Multiply (2r) by (4r^2 - 6rs + 9s^2), which gives (8r^3 - 12rs + 18s^2).
- Subtract (8r^3 - 12rs + 18s^2) from (8r^3 + 27s^3), which leaves (12rs - 9s^2).
- Bring down the next term (27s^3) and repeat.

Now, divide (12rs) by (4r^2), which gives (3s).

Multiply (3s) by (4r^2 - 6rs + 9s^2), which gives (12rs - 18s^2 + 27s^3).

Subtract (12rs - 18s^2 + 27s^3) from (12rs - 9s^2), which leaves (9s^2).

Since the degree of (9s^2) is less than the degree of (4r^2 - 6rs + 9s^2), the division is complete.

Therefore, the quotient is (2r + 3s) and the remainder is (9s^2).

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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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