# How do find the quotient of #(2x^3 − 3x 2 + x − 6) ÷ (x − 4)#?

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How do find the quotient of #(2x^3 − 3x^2 + x − 6) ÷ (x − 4)# ?

How do find the quotient of

The quotient polynomial :

Using synthetic division :

Hence ,

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To find the quotient of (2x^3 − 3x^2 + x − 6) ÷ (x − 4), you can use long division. Here are the steps:

- Divide the first term of the dividend (2x^3) by the first term of the divisor (x). The result is 2x^2.
- Multiply the divisor (x − 4) by the quotient obtained in step 1 (2x^2). The result is 2x^3 − 8x^2.
- Subtract the result obtained in step 2 from the dividend (2x^3 − 3x^2 + x − 6) to get the new dividend: (-8x^2 + x − 6).
- Repeat steps 1-3 with the new dividend (-8x^2 + x − 6).
- Divide the first term of the new dividend (-8x^2) by the first term of the divisor (x). The result is -8x.
- Multiply the divisor (x − 4) by the quotient obtained in step 5 (-8x). The result is -8x^2 + 32x.
- Subtract the result obtained in step 6 from the new dividend (-8x^2 + x − 6) to get the new dividend: (33x − 6).
- Repeat steps 5-7 with the new dividend (33x − 6).
- Divide the first term of the new dividend (33x) by the first term of the divisor (x). The result is 33.
- Multiply the divisor (x − 4) by the quotient obtained in step 9 (33). The result is 33x − 132.
- Subtract the result obtained in step 10 from the new dividend (33x − 6) to get the remainder: (126).
- The quotient is the sum of the quotients obtained in each step: 2x^2 - 8x + 33.

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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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