# How do you divide #(4x^3+7x^2-9x+15)/(x+1) #?

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To divide (4x^3+7x^2-9x+15) by (x+1), you can use long division. Here are the steps:

- Divide the first term of the dividend (4x^3) by the first term of the divisor (x). This gives you 4x^2.
- Multiply the entire divisor (x+1) by the quotient obtained in step 1 (4x^2). This gives you 4x^3+4x^2.
- Subtract the result obtained in step 2 from the original dividend (4x^3+7x^2-9x+15) to get the remainder. The remainder is (-3x^2-9x+15).
- Bring down the next term from the dividend (-3x^2) and repeat steps 1-3.
- Divide (-3x^2) by (x) to get -3x.
- Multiply the entire divisor (x+1) by the quotient obtained in step 5 (-3x). This gives you -3x^2-3x.
- Subtract the result obtained in step 6 from the remainder obtained in step 3 (-3x^2-9x+15) to get the new remainder. The new remainder is (-6x+15).
- Bring down the next term from the dividend (-6x) and repeat steps 1-3.
- Divide (-6x) by (x) to get -6.
- Multiply the entire divisor (x+1) by the quotient obtained in step 9 (-6). This gives you -6x-6.
- Subtract the result obtained in step 10 from the new remainder obtained in step 7 (-6x+15) to get the final remainder. The final remainder is (21).
- The quotient is the sum of the quotients obtained in steps 1, 5, and 9, which is (4x^2-3x-6).
- The final result is the quotient (4x^2-3x-6) with the remainder (21) written as a fraction over the divisor (x+1). Therefore, the division of (4x^3+7x^2-9x+15) by (x+1) is (4x^2-3x-6) with a remainder of 21 over (x+1).

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To divide ((4x^3 + 7x^2 - 9x + 15)) by ((x + 1)), perform polynomial long division or synthetic division:

Using polynomial long division:

- Divide the leading term of the dividend by the leading term of the divisor. This gives the first term of the quotient.
- Multiply the divisor by the first term of the quotient, and subtract this product from the dividend.
- Repeat steps 1 and 2 with the new dividend until the degree of the remainder is less than the degree of the divisor.

Using synthetic division:

- Write down the coefficients of the dividend in descending order.
- Write down the root of the divisor (in this case, -1) outside a vertical bar.
- Bring down the first coefficient.
- Multiply the root by the result and write it below the next coefficient.
- Add vertically and continue the process until all coefficients are brought down and added.
- The final line of numbers represents the coefficients of the quotient polynomial, and the last number is the remainder.

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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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