Simplify using long division(please show work so I understand)
1.Divide (72-8x^2+4x^3-36x)by (x-3)
2.Divide (8b^3-6) by (2b-1)
It is very hard to show the steps in this format
here is a page that explains it well
http://www.purplemath.com/modules/polydiv3.htm
and here is one has many "images" of different divisions, you can study them
http://www.google.com/search?q=long+algebraic+division&tbm=isch&tbo=u&source=univ&sa=X&ei=9VtsUcWJFo2H2AWx04DABQ&ved=0CHEQsAQ&biw=1659&bih=936#imgrc=_
Sure! I can help you with both of these problems. Let's start with the first one:
1. Divide (72 - 8x^2 + 4x^3 - 36x) by (x - 3)
To use long division, we'll follow these steps:
- Divide the highest degree term of the dividend (in this case, 4x^3) by the highest degree term of the divisor (x), which gives us 4x^2 as our quotient term.
- Multiply the divisor (x - 3) by the quotient term (4x^2) to get the product.
- Subtract the product from the dividend.
- Bring down the next term and repeat the process until we can no longer divide.
Let's break it down step by step:
4x^2
____________________
(x - 3) | 4x^3 - 8x^2 - 36x + 72
- Divide 4x^3 by x, which gives us 4x^2. Write this as the first term of the quotient above the line.
- Multiply (x - 3) by 4x^2 to get 4x^3 - 12x^2. Write this below the dividend.
- Subtract 4x^3 - 12x^2 from 4x^3 - 8x^2 to get 4x^2 + 4x^2 = 8x^2. Write this below the line.
- Bring down the next term, which is -36x.
- Divide 8x^2 by x to get 8x. Write this as the second term of the quotient above the line.
- Multiply (x - 3) by 8x to get 8x^2 - 24x. Write this below the line.
- Subtract 8x^2 - 24x from 8x^2 - 36x to get -12x. Write this below the line.
- Bring down the next term, which is +72.
- Divide -12x by x to get -12. Write this as the third term of the quotient above the line.
- Multiply (x - 3) by -12 to get -12x + 36. Write this below the line.
- Subtract -12x + 36 from -12x + 72 to get 36. Write this below the line.
Since we can no longer divide, the final quotient is 4x^2 + 8x - 12, and the remainder is 36.
Now let's move on to the second problem:
2. Divide (8b^3 - 6) by (2b - 1)
Using the same steps, let's break it down:
4b^2
_______________________
(2b - 1) | 8b^3 + 0b^2 + 0b - 6
- Divide 8b^3 by 2b, which gives us 4b^2. Write this as the first term of the quotient above the line.
- Multiply (2b - 1) by 4b^2 to get 8b^3 - 4b^2. Write this below the dividend.
- Subtract 8b^3 - 4b^2 from 8b^3 + 0b^2 to get 4b^2 + 0b^2 = 4b^2. Write this below the line.
- Bring down the next term, which is 0b (or just 0).
- Divide 4b^2 by 2b to get 2b. Write this as the second term of the quotient above the line.
- Multiply (2b - 1) by 2b to get 4b^2 - 2b. Write this below the line.
- Subtract 4b^2 - 2b from 4b^2 + 0b to get 2b. Write this below the line.
- Bring down the next term, which is -6.
- Divide 2b by 2b to get 1. Write this as the third term of the quotient above the line.
- Multiply (2b - 1) by 1 to get 2b - 1. Write this below the line.
- Subtract 2b - 1 from 2b - 6 to get -5. Write this below the line.
Since we can no longer divide, the final quotient is 4b^2 + 2b + 1, and the remainder is -5.
I hope this helps you understand the process of long division. Let me know if you have any further questions!