Using Regular Division to solve?

Question

(2x^5+13x^4+17x^3-7x^2+4x-33) / (x+3)

Answer 1

We can't really show you how to do it here (it gets really messy in type), but here's a great page that shows you how to do it:

http://www.purplemath.com/modules/polydiv2.htm

The answer is
2x^4 + 7x^3 - 4x^2 + 5x - 11

Answer 2

The correct answer is the first one shown.

You do synthetic division by making it look like long division with the numbers replaced by the actual values:

.......______________________________
x+3 ) 2x^5 + 13x^4 + 17x^3 - 7x^2 + 4x - 33

and doing the division the same way, with the small adjustments that become obvious. For instance, here you look at the highest power of x in (x+3) and see it is 1. So start putting your quotient above the x^(highest power - 1) = x^4 place. As to the actual quotient component to put there, take the leftmost existing term (2x^5) and divide it by the highest power of x term in the (x+) term: 2x^5 / x^1 = 2x^4. So 2x^4 goes above the +13x^4 term and you multiply (x+3) by it to get the value to list below and subtract from the 2x^5 + 13x^4...: 2x^4 * (x + 3) = 2x^5 + 6x^4. Subtract that to get the remainder of 7x^4. Bring down the "next digit" (next term), like in long division: +17x^3 so you have 7x^4 + 17x^3. Again, use the 7x^4 / x^1 = 7x^3 to find the next component of the quotient. Continue on following this approach. The only real "trap" to look out for is having something like the next remainder and "bring down": -4x^3 - 7x^2 and needing to subtract: -4x^3 - 12x^2. Many people properly realize the -4x^3 - (-4x^3) is the same as -4x^3 + 4x^3 = 0, but then move right and immediately do: -7x^2 - (-12x^2) = -19x^2 rather than realizing it is also like the first part: -7x^2 + 12x^2 = 5x^2. They think of the -12's "-" sign as the subtraction operator rather than as a sign, even though it is no longer "how much less than -4x^3" that concerns them but rather only the x^2's that are of interest.

Being careful of that kind of pitfall, synthetic division is incredibly simple and straightforward. Just a matter of taking care to avoid the pitfall and Bob's your uncle!

Answer 3

this is really long so i cant type it but what i remember i can try to explain it. if u know synthetic divison or have a graphin caculator. do it on there first so you what your answer should be.

idk how 2 ur specifically but:

Find:


The problem is written like this (note that, as explained above, the x term is included explicitly, regardless of the coefficient):


1. Divide the first term of the dividend by the highest term of the divisor. Place the result above the bar (x3 ÷ x = x2).



2. Multiply the divisor by the result you just obtained (the first term of the eventual quotient). Write the result under the first two terms of the dividend (x2 * (x-3) = x3 - 3x2).


3. Subtract the product you just obtained from the appropriate terms of the original dividend, and write the result underneath. This can be tricky at times, because of the sign. ((x3-12x2) - (x3-3x2) = -12x2 + 3x2 = -9x2) Then, "pull down" the next term from the dividend.


4. Repeat the previous three steps, except this time use the two terms that you have just written as the dividend.


5. Repeat step 4. This time, there is nothing to "pull down".


The polynomial above the bar is the quotient, and the number left over (-123) is the remainder.

Answer 4

qoutient = 2x^4+7x^3-4x^2+5x-11
remainder = 0

Answer 5

The first answer is right.

I used long division to solve it.

Answer 6

I'm not entirely sure how to solve it. But you could go to www.hotmath.com and see how to solve a problem like that. Good luck!

Answer 7

**********2x^4 + 7x³ - 4x² + 5x - 11
___________________________________
(x + 3) | 2x^5 + 13x^4 + 17x³ - 7x² + 4x - 33
********| 2x^5 + 6x^4
****************|7x^4 + 17x³ - 7x² + 4x - 33
****************|7x^4 + 21x³
***********************|- 4x³ - 7x² + 4x - 33
***********************|- 4x³ - 12x²
******************************|5x² + 4x - 33
******************************|5x² + 15x
*************************************|- 11x - 33
*************************************|- 11x - 33


R = 0
Q(x) = 2x^4 + 7x³ - 4x² + 5x - 11
Hope you can follow this---difficult to type out.