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Hi! May someone please go through how to completely factor these questions?

1) m^2-15m+26

2) 4x^2 + 8x -12

3) 3x^2 + 5x + 2

4) 24y^3 + 68y^2 - 56y


Thank you so much! :D

(https://biology-forums.com/gallery/42/6_31_01_21_2_04_49.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=42460)

Here are the techniques I used:

Trial and Error

https://www.youtube.com/watch?v=iXyzSdryP98

Factoring by Decomposition

https://www.youtube.com/watch?v=SFQm9NCXG88

Hope you can watch them!

Thank you! I tried following the decomposition method video to try and solve 3x^2+5x+2 on my own.

1. I multiplied a by c leaving me with 6
2. I found the factors of 6, and found the 2 that add together to find 5 (2 & 3)
3. I plugged those back into my expression leaving me with 3x^2+2x+3x+2.
4. I separated them with brackets like it said in the video. (3x^2+2x)(+3x+2)
Then found a common factor for the first brackets, 1x. Then was left with +3x+2 on the other side. :-:)

In the video,  the other half was able to be factored out, but mine can’t as they aren’t the same. My answer is different from yours and I’m not sure how to get to your answer you found for my question #3

Post Merge: 3 years ago

I understand the process and answers of 1  & 2 just am a little lost in 3 & 4.

I made a mistake with my #3!

So let's continue with where you left-off:

1. I multiplied a by c leaving me with 6 ✔️
2. I found the factors of 6, and found the 2 that add together to find 5 (2 & 3) ✔️ (here's where I was wrong!)
3. I plugged those back into my expression leaving me with 3x^2+2x+3x+2. ✔️

4. I separated them with brackets like it said in the video. (3x^2+2x)(+3x+2)
Then found a common factor for the first brackets, 1x. Then was left with +3x+2 on the other side.

Now you common factor by grouping:

3x^2+2x+3x+2

Focusing on the blue: x(3x+2)
Focusing on the red: not common factorable

x(3x+2)+3x+2

Since the red is not common factorable, put parentheses around 3x+2

x(3x+2) + (3x+2)

Now common factor again the (3x+2):

(3x+2)(x + 1)

Thanks so much! I’ll go over mine again!

Post Merge: 3 years ago

In the very last part where you are common factoring (3x+2), where did the (x+1) come? I thought it would have just been x or 1x. Sounds like  silly question but I just want to know why it’s written that way :D

Here's the logic, imagine you have:

(x^2 + x)

if you common factor 'x', you get

x(x + 1)

you see how that 1 appeared? by factoring something out, doesn't mean it disappears, it just becomes 1 instead because factoring is like dividing each term by the factored term

so going back to x(3x+2) + (3x+2)

If I factor out (3x+2), you're left with x as the first term and 1 as the second term

does that make more sense?

Yes it does! Thanks! :D

Post Merge: 3 years ago

Hi again, sorry, can you go over what happened in quest #4 in the second row? I have the exact same when you factored out 4y from all terms but I’m confused where the two red numbers came from.