dividing monomials

Re: dividing monomials

You know that the answer must be of the form (ay + b) where a and b are some constants, and that the product then equals (ay+b)(y+7) = ay^2 + 7ay + by + 7b. Since the final term of the product is 14, b must be 2. Since the second power term has a coefficient of 1, a must be 1.

Hence, you get (y + 2) which works if you multiply it out.

Synthetic Division
You can also use synthetic division for general problems of this sort. Here is what it looks like but I'll let you follow the link if you want more detail which might be useful since my graphic skills are lacking on this board.

......___1_2___
1 7 ) 1 9 14
....... 1 7
....... -----
........... 2 14
........... 2 14
.......... --------
................. 0

so the answer is 1y + 2.

The real trick in division like this (or any other math problem in general) is to check your answer.

If (y^2+9y+14)/(y+7)=y+2
Then
(y+7)(y+2)=y^2+9y+14

if you do the division, then check. Verify your answer.

BTW your answer -10y+2 if you checked would be

(10y+2)(y+7)=10Y^2+(10*7+2*1)y+14=10y^2+72y+14 is not equal to y^2+9y+14. So you don't have to guess if (10y+2) is the wrong answer---you quickly know it's the wrong answer..

Engineer's link to synthetic division is good. Moreover, synthetic division is a good algorithm to use to practice spreadsheeting (Excel), however, IMO it reality algorithms are good only after you understand what your doing. In this case polynomial division,. and polynomial division is long division with algebraic expressions. There are many good links to this polynomial long division. One can be found here. (click on blue)

Rap

I would have done

(y^2+9y+14)/(y+7) = ay + b by inspection, so

y^2+9y+14 = (y+7) * (ay + b)

kinda tells you a = 1 and b = 2 straight away!

Simple factorisation on the top.

(y^2 + +9y + 14) / (y+7)

= (y + 7) (y + 2) / (y + 7)

The (y + 7) cancel out now and you;re left with

= (y + 2) / 1

Now what did the question say at the top? Did it say factorise completly or solve for "y"? If its the former then stop at (y + 7) (y + 2) / (y + 7)