Question

Math help please :)

Answer 1

\[4x^3+24x^2-x-6=0\] factor by grouping. I'm write down what I already have.

Answer 2

\[4x^2(x+6)\] this is all I have so far

Answer 3

I know theres a whole nother thing to be done

Answer 4

how u got 4x^2(x+6) the -6 is missing

Answer 5

what?

Answer 6

I'm not completely finished. which is why im here :)

Answer 7

where did the -6 go

Answer 8

oh my fault my fault

Answer 9

@dude

Answer 10

@ukulelegirl

Answer 11

and I got the 4 from factoring 4 and 24

Answer 12

and then I brought an \(x^2\) down

Answer 13

then i put parenthesis and brought down what I had left. Which is \(x+6\)

Answer 14

the x being from the x we never used and the 6 from 24 divided by 4

Answer 15

Now I'm stuck.

Answer 16

key word: factoring by grouping. when you factor by grouping, you split the expression into two groups.

4x^3 + 24x^2 - x - 6 = 0

splitting into two groups:

(4x^3 + 24x^2) - (x + 6) = 0

important: because of the subtraction, you have to change x - 6 to x + 6 in order to keep the value the same. I'm also going to write a 1* in front, for a reason you'll see later.

(4x^3 + 24x^2) - 1*(x + 6) = 0

now, we factor the first expression inside the parentheses

4x^2(x + 6) - 1*(x+6)

now, apply the opposite of the distributive property. if you have A*B - A*C you can factor out the A to get A(B-C). applying this logic to our problem:

4x^2(x + 6) - 1*(x+6) = (4x^2 - 1)(x+6)

from there, 4x^2 - 1 is a difference of squares, so factor that. once you have all three factors, set each factor equal to 0 to get the three possible x values.

Answer 17

Uhm I'm sorry. I'm a bit confused here...

Answer 18

starting from the beginning:

4x^3 + 24x^2 - x - 6 = 0

because we're using the method factoring by grouping, we split the expression into groups.

group 1, the first two terms: 4x^3 + 24x^2
group 2: the other two terms: x-6

we separate our groups with parentheses:

(4x^3 + 24x^2) - (x + 6)

that middle subtraction sign in front of the second group makes it a bit tricky. in order to keep the value - x - 6, we can't write - (x-6) because this is actually equal to -x + 6 after distributing the negative sign.

do you understand this part so far?

Answer 19

Yes I got all that up until the second group. I done factored out all of the first group.

Answer 20

I factored out \(4x^2(x+6)\) this is all i got so far.

Answer 21

good, so you factored out the first group. now, combining this with the second group

4x^2(x+6) - 1*(x+6)

notice how both terms have a (x+6). Now, looking at the other parts of the expression, remaining part is 4x^2 - 1. (I wrote the 1* in front of (x+6) to make this more clear.)

you can factor out the (x+6) to get:

(4x^2 - 1)(x+6)

Answer 22

Yes. I guess that sorta makes sense.

Answer 23

this can be a little hard to see, so try thinking about this in reverse:

A(B-C) = A*B - A*C

treat (x-6) as your A value, 4x^2 as your B value, 1 as your C value

so (x+6)(4x^2 - 1) = (x+6)(4x^2) - (x+6)(1)

and we just did the reverse of that, we took (x+6)(4x^2) - (x+6)(1) and factored it into (x+6)(4x^2 - 1)

Answer 24

Mhm.

Answer 25

from there:

(x+6)(4x^2 - 1)

(4x^2-1) is a difference of squares. factoring gives us (2x+1)(2x-1)

and in total we have: (x+6)(2x+1)(2x-1) = 0

so in order to solve for x, set (x+6) = 0, 2x + 1 = 0, 2x - 1 = 0 and get the three x values

Answer 26

no mean to interrupt but someone keeps posting zoom links in the all sub.

Answer 27

actually it's just asking to factor so I think you can probably stop here: (x+6)(2x+1)(2x-1) = 0

Answer 28

Ok thanks for the help.