What Is The Quotient (3x4 2013 4x2 + 8x 2013 1) \Xf7 (X 2013 2)?

What is the quotient (3x4 – 4x2 + 8x – 1) ÷ (x – 2)?

Answer:

$3x^{3} +6x^{2} +8x + 24 +\frac{47}{x-2}$

Step-by-step explanation:

I used synthetic division here.

So first get the constant of the denominator which is -2 and change the reverse the sign, so it will become 2.

Next get all the coefficients of the numerator. Which are:

3, 0, -4, 8, and -1

Notice that the exponent from the equation doesnt have $x^{3}$ so it will become 0. It is called missing term.

Now, lets solve.

First, separate the constant of the denominator by drawing a line or box.

Then align the coefficients of the numerator.

The operation will be addition.

It looks like this:

2I 3 0 -4 8 -1

Now bring down the first number which is 3. (You will not bring down the 2, because it will be used for multiplication.)

2I 3 0 -4 8 -1

Then multiply it by the constant of the denominator which is 2,

2I 3 0 -4 8 -1

+ 6

Then add,

2I 3 0 -4 8 -1

+ 6

3 6

Next multiply the product and add it to the next term. Repeat it until you last the last number.

2I 3 0 -4 8 -1

+ 6 12 16 48

3 6 8 24 47

The last number will be the remainder.

Now lets subtract the exponent with 1. And substitute the new coefficient.

$3x^{3} +6x^{2} +8x + 24$

As I said "the last term will be remainder."

You can write r. 47 or $\frac{47}{x-2}$ (it has x-2 because it is not divisible)

So the final answer is:

$3x^{3} +6x^{2} +8x + 24 +\frac{47}{x-2}$

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