Can someone help me understand what to do here

[slender sun]

Do you mean for question 2?

[heady bluff]

For both

My teacher ended up just anwsering the first few questions when trying to explain it to me

[slender sun]

d) 8x^2 - 42x + 27

Step 1: Multiply 8 by 27:
8*27 = 216

Step 2: Find a multiple of 216 that’ll give you the sum of - 42:

1 216
2 108
3 72
4 54
6 36 <—

Step 3: Rewrite the multiple so it still multiplies to 216 but the sum equates too - 42:

-6 -36

Step 4: Rewrite the equation:

8x^2 - 6x - 36x + 27

Step 5: Drop the middle sign and factor out both parts:

2x(4x -3) - 9(4x - 3)

Step 5: Change into factor forms

(2X - 9) (4x - 3)

⬆️
Reply if you got any questions about a step

[heady bluff]

What do you mean drop the middle sign?

[slender sun]

Step 4: Rewrite the equation:

8x^2 - 6x “-” 36x + 27

Step 5: Drop the middle sign and factor out both parts:

2x(4x -3) “-” 9(4x - 3)

Idrk how to explain it, just knows it’ll be between the two numbers that are the multiple of 216

[heady bluff]

Ok so just like separate the question in half

[slender sun]

Yeah, basically!

[heady bluff]

How did you go from
2x(4x -3) -9(x -3)
To
(2x -9) (4x -3)

If you could just explain it in more detail

[heady bluff]

Also thanks for the help

[slender sun]

No problem! As for the previous question, I cannot really explain it in any other way except that the two equate each other.

I mean the only other way is to just say
(4x -3) is similar in both, so you combine the two and what are you left with? 2x-9

[heady bluff]

I don’t really get what you mean by they are similar in both

[heady bluff]

Hey @slender sun is the anwser for question e)
(-4n + 21) (n + 1)

[slender sun]

E) -4n^2 - 17n+ 15

Step 1: Multiply -4 by 15:
-4 * 15 = -60

Step 2: Find a multiple of -60 that’ll give you the sum of 17:

-3 20 <—
Step 3: Rewrite the equation:

-4n^2 -3n “+” 20n + 15

Step 4: Drop the middle sign and factor out both parts:

-N(4n + 3) + 5(4n +3)

Step 5: Change into factor forms
(-N+5)(4n+3)

I got this