Question

Which is the correct step below for using the grouping method to factor the following polynomial? 5xy + 15x - 2y - 6
A. x(5y + 15) - 1(2y + 6)
B. 5x(y + 3) + 2(y + 3)
C. 5x(y + 3) - 2(y + 3)
D. 5x(y - 3) - 2(y - 3)

Answer 1

I think its B but not sure?

Answer 2

Well, expand B, what do you get?

\[5x(y+3) + 2(y+3) =\]

Answer 3

Hint: for it to be a correct step, it must not change the value of the thing being factored!

Answer 4

Another hint, which you probably don't need, is that the two groups, after factoring, must have a common factor (so A is not an option)

Answer 5

So I was right? sorry it took me so long to reply

Answer 6

Expand B. What do you get?

Answer 7

5x(y + 3) + 2(y + 3) this is what I got. Is that what you wanted? Sorry I just learned how to do this! :P

Answer 8

Multiply it out!

Answer 9

(5x+2)(y+3)?

Answer 10

NO...

What is \[5x(y+3)=\]
What is \2(y+3)=\]
Add them together. What do you get?

Answer 11

Sorry, second equation should be \[2(y+3)=\]

Answer 12

5xy+15x+2y+6

Answer 13

Yes, and is that what you set out to factor?

Answer 14

ohhh I see! I added them and I got what the original polynomial was!

Answer 15

yes!

Answer 16

No, it's not!
\[5xy + 15x - 2y - 6\] is what you are supposed to factor!

Answer 17

oh...... hehe! im really bad at math if you haven't noticed already.

Answer 18

bad at math may not really be true so much as a failure to look very closely...

Answer 19

yeah your right!

Answer 20

convince yourself of the correctness of each step along the way and you'll magically get a lot better at math :-)

Answer 21

so, what's your new choice for the correct answer? check it in the same fashion as we did here...

Answer 22

I am thinking C?

Answer 23

If you checked it in the same way, you should be more certain than that :-)

Answer 24

\[5x(y + 3) - 2(y + 3) = 5x*y + 5x*3 -2*y -2*3 = 5xy+15x-2y-6\]
That looks like a good answer!

Answer 25

I have a 99.8% that its C!

Answer 26

There you go. An old math teacher of mine liked to respond to answers such as "I am thinking C?" with "is that an answer, or a prayer?" :-)

Answer 27

So it is 100% C!?!

Answer 28

Very good!

So the next step here would be
\[5x(y+3)-2(y+3) = (y+3)(5x-2)\]

And we check our work:

\[(y+3)(5x-2) = y(5x-2) + 3(5x-2) = 5xy -2y + 15x -6 = 5xy + 15x -2y -6\checkmark\]

Answer 29

@#$@#% OS.
\[5xy-2y+15x-6 = 5xy+15x-2y-6\checkmark\]

Answer 30

Do you have any questions about this factoring by grouping business?

Answer 31

Thank you soooooo much! Nope! Thank you! :D

Answer 32

Okay, remember to check your work with a skeptical eye :-)