This problem was on a test and I got it wrong, and if I do it over I get half the credit back, but I need help with it plz.
(11x^2+2x^3+14+17x)/(2x+5)
My algebra teacher didn't even go over this lesson (we skipped it) and it was on the test. She says it's long division, but I don't know how to solve this problem that way. Any help is greatly appreciated!!
[put the numerator in the decending powers of x...
2x^3+11x^2+17x+14
Now divide 2x + 5 into it. Doing it here is foolhardy,but look at these examples.
http://www.purplemath.com/modules/polydiv2.htm
That helped me SOOOO much!! Thanks for all your help, you're the best online help! (I wish I knew this before the test! LOL)
I'm glad I could help you! I understand that long division can be confusing, especially if you haven't been taught it before. Here's how you can solve this problem using long division:
First, rewrite the expression with the terms in descending order of powers of x:
2x^3 + 11x^2 + 17x + 14
Now, take the first term of the polynomial (2x^3) and divide it by the first term of the divisor (2x). This gives you x^2, which is the first term of your quotient.
x^2
---------------------
2x + 5 | 2x^3 + 11x^2 + 17x + 14
Next, multiply the divisor (2x + 5) by the x^2 quotient (x^2) to get 2x^3 + 5x^2. Subtract this from the original polynomial:
x^2
---------------------
2x + 5 | 2x^3 + 11x^2 + 17x + 14
- (2x^3 + 5x^2)
---------------
6x^2 + 17x + 14
Now, bring down the next term (17x) and repeat the process. Divide the new polynomial (6x^2 + 17x + 14) by the first term of the divisor (2x), which gives you 3x.
x^2 + 3x
---------------------
2x + 5 | 2x^3 + 11x^2 + 17x + 14
- (2x^3 + 5x^2)
---------------
6x^2 + 17x + 14
- (6x^2 + 15x)
---------------
2x + 14
Now, bring down the last term (14) and divide it by the first term of the divisor (2x), which gives you 7.
x^2 + 3x + 7
---------------------
2x + 5 | 2x^3 + 11x^2 + 17x + 14
- (2x^3 + 5x^2)
---------------
6x^2 + 17x + 14
- (6x^2 + 15x)
---------------
2x + 14
- (2x + 5)
------------
9
At this point, there are no more terms to bring down, and your remainder is 9.
Therefore, the quotient is x^2 + 3x + 7, and the remainder is 9.
I hope this explanation helps you understand the process of solving the problem using long division. If you have any further questions, feel free to ask!