# How do you divide #(x^2 - 2x - 15)/(x + 3)# using polynomial long division?

Answer 2 of 2

Have a look at the method. It shows a useful 'trick'.

Not all questions permit this approach of solution!

This can be factored into:

Substitute expression (2) into expression (1)

If you were investigating values then this produces a problem. You are not mathematically allowed to divide by 0.

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Answer 1 of 2

Using polynomial long division.

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To divide (x^2 - 2x - 15) by (x + 3) using polynomial long division, follow these steps:

- Write the dividend (x^2 - 2x - 15) and the divisor (x + 3) in long division format.
- Divide the first term of the dividend (x^2) by the first term of the divisor (x). The result is x.
- Multiply the divisor (x + 3) by the result obtained in step 2 (x), and write the product (x^2 + 3x) below the dividend.
- Subtract the product obtained in step 3 from the dividend. (x^2 - 2x - 15) - (x^2 + 3x) = -5x - 15.
- Bring down the next term from the dividend (-5x) and rewrite it next to the result obtained in step 2 (x).
- Divide the new expression (-5x) by the first term of the divisor (x). The result is -5.
- Multiply the divisor (x + 3) by the result obtained in step 6 (-5), and write the product (-5x - 15) below the previous subtraction.
- Subtract the product obtained in step 7 from the expression (-5x - 15). (-5x - 15) - (-5x - 15) = 0.
- There is no remainder, and the division is complete. The quotient is x - 5.

Therefore, (x^2 - 2x - 15)/(x + 3) = x - 5.

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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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