# What is the remainder from the following: F(x) = 2x^4 - 3x^3 - 5x^2 + 3x + 8 divided by x - 2 ?

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### 1 Answer

There are a few methods to solve this but synthetic division is probably the best and, once you have learnt the method, it can be applied for all calculations of this nature.

There are some important things you need to remember:

A co-efficient is the number you see in front of the x. If you have `x^2` for example, the co-efficient is 1.

The equation or expression must be in the standard form which means it must be in sequence - decreasing powers of x - (`x^4 x^3 x^2)` and so on.

The factor is the divisor - in this case (x - 2), which means that x=2 and you will use the value '2' to solve.

The first factor is always brought down (to line 3) as it is - no change so for our calculation the 2 will be brought down as 2

F(x) = 2x^4 - 3x^3 - 5x^2 + 3x + 8 divided by x - 2 ?

`f(x)= ( 2x^4 - 3x^3 - 5x^2 + 3x + 8)/ (x-2)`

The most common way to do this is like an upside down division sum - but I don't know how to do that here so make a table. You are first working with lines 1 and 3 and answers go in line 2.

2 [ `|__2 -3 -5 +3 +8` ] line 1

4 2 -6 -6 line 2

`|__` 2 1 -3 -3 2] line 3

1. bring down the first number; in this case 2 down to line 3

2. Multiply the 2 by the factor (which in this case is also 2)

3.Place the answer (4) on line 2 (below the -3)

4. Add the 4 to the number in line 1 (in this case -3). This equals 1 right! -3 + 4 = 1

5. Write the 1 from point 4 on line 3. Now repeat the process from points 2 to 5 using the factor 2 and the new number in line 3. I'll talk you through one more of these.

So multiply the factor (2) by the new number on line 3,ie 1. 2 x 1=2

Place the answer on line 2 (below the -5) .

Add the -5 and the 2. -5+2 = -3

Write the -3 on line 3. Now repeat the process until you have finished.

You will get a **remainder of 2**