Can anyone please teach me how to divide polynomials using long division?
It's quite confusing. Like give me a problem to solve and guide me through it.
I suggest you play around at http://www.calc101.com
Just click on the "long division" button and you can see all the details. It's just like regular numeric long division, but you have to keep track of the separate powers of x, just as you have to line up the columns of digits in regular long division.
OK, thank you! :)
Sure! I can guide you through the process of dividing polynomials using long division. Let's start with a simple example:
Problem: Divide the polynomial 3x^3 + 4x^2 - 5x + 2 by the polynomial x - 1.
Step 1: Arrange the polynomials in descending order of degree:
3x^3 + 4x^2 - 5x + 2 divided by x - 1
Step 2: Start the long division process by dividing the highest-degree term of the dividend (3x^3) by the highest-degree term of the divisor (x). Place the result above the division symbol:
________
x - 1 | 3x^3 + 4x^2 - 5x + 2
3x^2
Step 3: Multiply the divisor (x - 1) by the quotient (3x^2) and write the result below the dividend, lining up like terms:
________
x - 1 | 3x^3 + 4x^2 - 5x + 2
3x^2 - 3x^2
Step 4: Subtract the line in Step 3 from the original dividend. Bring down the next term (in this case, -5x):
________
x - 1 | 3x^3 + 4x^2 - 5x + 2
3x^2 - 3x^2
--------------
- 5x
Step 5: Repeat steps 2-4 with the new dividend (-5x):
________
x - 1 | 3x^3 + 4x^2 - 5x + 2
3x^2 - 3x^2
--------------
- 5x + 5x
Step 6: After subtracting, the remainder is 0, meaning there are no more terms to bring down. We have successfully divided the polynomial.
Step 7: Write the final answer as the quotient plus any remaining constant terms from the original dividend. In this case, the quotient is 3x^2, so the final answer is:
3x^2
Therefore, the polynomial 3x^3 + 4x^2 - 5x + 2 divided by x - 1 is equal to 3x^2.
I hope this explanation helps you understand how to divide polynomials using long division!