# How do you divide #(n^3 + 2n^2 - n - 2) # by #(n^2 - 1)#?

Refer to explanation

We have that

#(n^3 + 2n^2 - n - 2)/(n^2 - 1)=(n^3-n+2(n^2-1))/(n^2-1)= (n(n^2-1)+2(n^2-1))/(n^2-1)=((n^2-1)*(n+2))/(n^2-1)=n+2#

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To divide the polynomial (n^3 + 2n^2 - n - 2) by (n^2 - 1), we perform polynomial long division or synthetic division.

Using polynomial long division:

- Divide the first term of the dividend by the first term of the divisor.
- Multiply the entire divisor by the result obtained in step 1.
- Subtract the result obtained in step 2 from the dividend.
- Repeat steps 1-3 until the degree of the remainder is less than the degree of the divisor.

Using synthetic division:

- Write down the coefficients of the dividend and divisor.
- Change the sign of the constant term of the divisor.
- Perform synthetic division as usual.
- Write down the quotient obtained.

After performing polynomial long division or synthetic division, we obtain the quotient (n + 3) and the remainder (2n + 1). Therefore, the result of dividing (n^3 + 2n^2 - n - 2) by (n^2 - 1) is (n + 3) with a remainder of (2n + 1).

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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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- How do you use synthetic division #x^4-9x^3+5x^2-7x+10, a=-4#?

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