# How do you divide #(5x^3-x^2 + 7x – 6) / (x-1) # using polynomial long division?

Divide this using long division:

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To divide (5x^3 - x^2 + 7x - 6) by (x - 1) using polynomial long division, follow these steps:

- Arrange the dividend (5x^3 - x^2 + 7x - 6) and the divisor (x - 1) in descending order of powers of x.
- Divide the first term of the dividend (5x^3) by the first term of the divisor (x). The result is 5x^2.
- Multiply the divisor (x - 1) by the result obtained in step 2 (5x^2). The product is 5x^3 - 5x^2.
- Subtract the product obtained in step 3 from the dividend. (5x^3 - x^2 + 7x - 6) - (5x^3 - 5x^2) simplifies to 4x^2 + 7x - 6.
- Bring down the next term from the dividend, which is 7x.
- Divide the first term of the new dividend (4x^2) by the first term of the divisor (x). The result is 4x.
- Multiply the divisor (x - 1) by the result obtained in step 6 (4x). The product is 4x^2 - 4x.
- Subtract the product obtained in step 7 from the new dividend. (4x^2 + 7x - 6) - (4x^2 - 4x) simplifies to 11x - 6.
- Bring down the next term from the new dividend, which is -6.
- Divide the first term of the new dividend (11x) by the first term of the divisor (x). The result is 11.
- Multiply the divisor (x - 1) by the result obtained in step 10 (11). The product is 11x - 11.
- Subtract the product obtained in step 11 from the new dividend. (11x - 6) - (11x - 11) simplifies to 5.
- There are no more terms left in the dividend, so the division is complete.
- The quotient is 5x^2 + 4x + 11, and the remainder is 5.

Therefore, (5x^3 - x^2 + 7x - 6) divided by (x - 1) using polynomial long division is equal to 5x^2 + 4x + 11 with a remainder of 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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