SOLUTION: Help me perform the indicated operation? 2y^2-11y+16/2y+3

Question 886268: Help me perform the indicated operation?
2y^2-11y+16/2y+3
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it appears that you have to use long division.

the solution i got was y - 7 + 37/(2y+3) which can also be stated as y - 7 with a remainder of 37.

let's see if that works.

you multiply (2y+3) by (y-7) and you get 2y^2 - 11y - 21.

add in the remainder of 37 and you get 2y^2 - 11y + 16

since that's your original equation, your solution is correct.

if you need a tutorial on how to do polynomial long division, then check this out.

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

in your problem, i did the following:

divide 2y + 3 into 2y^2 - 11y + 16

your divisor is 2y + 3 and your dividend is 2y^2 - 11y + 16

2y goes into 2y^2 y times.

y is the first term in your solution.

multiply 2y + 3 by y and you get 2y^2 + 3y

subtract 2y^2 + 3y from 2y^2 - 11y + 16 and you get -14y + 16

your divisor is 2y + 3 and your dividend is not -14y + 16

2y goes into -14y -7 times.

-7 is the second term in your solution.

multiply 2y + 3 by -7 and you get -14y - 21

subtract -14y - 21 from -14y + 16 and you get 37.

your divisor is 2y + 3 and your dividend is not 37.

since the degree of your dividend is less than the degree of your divisor, you are done and 37 is your remainder.

your solution is y - 7 with a remainder of 37 as stated above.

this can also be shown as y - 7 + 37/(2y+3)

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