# How do you find the quotient of #(a^2+a-12)div(a-3)#?

The quotient is

Factorise first:

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To find the quotient of (a^2+a-12) divided by (a-3), you can use long division or synthetic division.

Using long division:

- Divide the first term of the numerator (a^2) by the first term of the denominator (a). This gives a as the first term of the quotient.
- Multiply the entire denominator (a-3) by the first term of the quotient (a), and subtract the result from the numerator (a^2+a-12).
- Bring down the next term (-12) from the numerator.
- Repeat the process by dividing the first term of the new numerator (a^2-2a) by the first term of the denominator (a), and continue until there are no more terms left in the numerator.
- The resulting quotient is a+4.

Using synthetic division:

- Write the coefficients of the numerator (1, 1, -12) and the divisor (1, -3) in descending order.
- Bring down the first coefficient (1) from the numerator.
- Multiply the divisor (1, -3) by the value brought down (1), and write the result below the next coefficient (-3).
- Add the corresponding coefficients (-3 and 1) and write the sum (-2) below the line.
- Repeat the process by multiplying the divisor (1, -3) by the new value (-2), and continue until there are no more coefficients left.
- The resulting quotient is a+4.

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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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