what is (6x^2+28x+29)/ (2x+6)?

Question

what is (6x^2+28x+29)/ (divided) (2x+6)? and explain the steps in doing this problem, i would greatly appreciate it.

Answer 1

Set it up like a long division sum.
Don't worry about the dots - that just for spacing
as I don't think a lot of spaces will work properly.
I just hope the dots work, or it could look messy.

........... Answer goes here
..........┌──────────
2x + 6 | 6x^2 + 28x + 29

1) Divide 2x into 6x^2 to get 3x.
That's the first part of the answer.
............ 3x
..........┌──────────
2x + 6 | 6x^2 + 28x + 29

2) Multiply 3x by 2x and 3x by 6.
Put the answers underneath the dividend.

............ 3x
..........┌──────────
2x + 6 | 6x^2 + 28x + 29
.......... | 6x^2 + 18x

3) Now subtract bottom from top.
6x^2 - 6x^2 = 0, so leave it clear.
28x - 18x = 10x. Put 10x under the 18x.
Also, bring down the 29.

............ 3x
..........┌──────────
2x + 6 | 6x^2 + 28x + 29
.......... | 6x^2 + 18x
.......... | ...........10x + 29

4) Now we start again by dividing 2x into
the new dividend, 10x + 29.
2x into 10x goes 5, so add 5 to the answer.

5) Then multiply 5 by 2x and 5 by 6 and
put the results under 10x + 29.

6) Subtract : 10x - 10x = 0 and 29 - 30 = -1
You'll end up with :

............ 3x + 5
..........┌──────────
2x + 6 | 6x^2 + 28x + 29
.......... | 6x^2 + 18x
.......... | ...........10x + 29
.......... | .......... 10x + 30
.......... | ..................... -1

This is as far as you can go,
so the remainder is -1 / (2x + 6)

So the answer to (6x^2 + 28x + 29) / (2x + 6) is :

3x + 5 - 1/(2x + 6)

Answer 2

There's nothing more to do with this expression. (2x + 6) doesn't factor into (6x^2 + 28x + 29), so you've gone as far as you can go with it.

Answer 3

3x+5 and -1/(2x+6) is the remainder

Answer 4

= 3x(2x+6)+5(2x+6)-1
= (2x+6)(3x+5)-1

So Ans. should be 3x+5