# How do you divide #(5m^3 - 7m^2 + 14) / (m^2 - 2)#?

The quotient is

We perform a long division

Therefore,

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To divide (5m^3 - 7m^2 + 14) by (m^2 - 2), we can use polynomial long division.

First, we divide the highest degree term of the numerator (5m^3) by the highest degree term of the denominator (m^2). This gives us 5m as the first term of the quotient.

Next, we multiply the entire denominator (m^2 - 2) by the first term of the quotient (5m), which gives us 5m^3 - 10m.

We then subtract this result from the numerator (5m^3 - 7m^2 + 14) to get -3m^2 + 14.

We repeat the process by dividing the highest degree term of the new numerator (-3m^2) by the highest degree term of the denominator (m^2), resulting in -3m as the next term of the quotient.

Multiplying the entire denominator (m^2 - 2) by -3m gives us -3m^3 + 6m.

Subtracting this from the new numerator (-3m^2 + 14) gives us 20m + 14.

We divide the highest degree term of this new numerator (20m) by the highest degree term of the denominator (m^2), resulting in 20 as the final term of the quotient.

Multiplying the entire denominator (m^2 - 2) by 20 gives us 20m^2 - 40.

Subtracting this from the new numerator (20m + 14) gives us 54.

Since the degree of the new numerator (54) is less than the degree of the denominator (m^2 - 2), we have completed the division.

Therefore, the quotient is 5m - 3 - (20 / (m^2 - 2)) and the remainder is 54.

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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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