95.6k views
4 votes
I have a question about polynomial division it is in the picture

I have a question about polynomial division it is in the picture-example-1
User SMAG
by
7.9k points

1 Answer

4 votes

To answer this question, we have to do the long division process for polynomials. We can do the operation as follows:

To do this division process, we have:

1. Divide the first term of the dividend by the first element of the divisor. They are:


(-4x^3)/(4x^2)=-x

2. Now, we have to multiply this result by the divisor, and the result will change its sign since we have to subtract that result from the dividend as follows:


-x\cdot(4x^2_{}-4x-4)=-4x^3+4x^2+4x

And since we to subtract this result from the dividend, we end up with:


-(-4x^3+4x^2+4x)=4x^3-4x^2-4x

3. Then we have the following algebraic addition:


\frac{\begin{cases}-4x^3+24x^2-15x-15 \\ 4x^3-4x^2-4x\end{cases}}{20x^2-19x-15}

4. Again, we need to divide the first term of the dividend by the first term of the divisor as follows:


(20x^2)/(4x^2)=5

5. And we have to multiply 5 by the divisor, and the result will be subtracted from the dividend:


5\cdot(4x^2-4x-4)=20x^2-20x-20

Since we have to subtract this from the dividend, we have:


-(20x^2-20x-20)=-20x^2+20x+20

6. And we have to add this algebraically to the dividend we got in the previous step:


\frac{\begin{cases}20x^2-19x-15 \\ -20x^2+20x+20\end{cases}}{x+5}

And this is the remainder of the division, x + 5.

As we can see from the division process, we got as:

1. The quotient: -x + 5


q=-x+5

2. The remainder: x + 5.


R=x+5

Since we have that the dividend = divisor * quotient + remainder.

Therefore, the result for this division is:


-4x^3+24x^2-15x-15=(4x^2-4x-4)\cdot(-x+5)+(x+5)

I have a question about polynomial division it is in the picture-example-1
User Gregorio
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories