# How do you use synthetic division and the Remainder Theorem to find #P(a)#, if #P(x) = 6x^4+19x^3-2x^2-44x-24# and #a=-2/3#?

Now, perform the following steps repeatedly until you run out of columns to work with:

- Multiply the last number written underneath the line by the number in the box to the upper-left, and write that product just above the line in the column to the right.
- Add the topmost coefficient number with the product you just wrote, and write that sum just under the line in the same column. This should be written just to the right of the rightmost number in the bottom row under the line.

Keep working in this manner until you run out of columns/numbers. I've color coded the sets of numbers in the worked out solution below:

To check (and completely defeating the purpose of using SD in the first place):

As you can see, SD calculations are far, far easier to do - sometimes even in your head!

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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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