Question

PLEASE HELP WITH FACTORING?
(worksheet attached)

Answer 1

I don't understand anything except for #5

Answer 2

Number 6: \[2x ^{2}-2x+10\]

Answer 3

could you please show the steps?

Answer 4

Number 7: The domain is all real numbers.

Answer 5

yeah sure.. gimme a sec

Answer 6

okay so for #6 you start with 2f(x)
It's easy to take things one step at a time:

f(x)= x^2+2x-1

^ now that and multiply it by 2:

2(x^2+2x-1) and you get:

2x^2+4x-2 <-- 2f(x)

Now you move onto 3g(x):

g(x)=2x-4

^ multiply that by three:

3(2x-4)

and you get: 6x-12 <--3g(x)

now you take 2f(x) and subtract 3g(x) from it:

2x^2+4x-2-(6x-12)

you distribute the negative sign first:

2x^2+4x-2-6x+12

and now you combine like terms:

2x^2-2x+10

Answer 7

For number 7:

we need to find out what f(g(x))

g(x): 7x+6

^ now take that and plug it into f(x):

3(7x+6)+2

and you distribute the 3 in front of the parenthesis:

21x+18+2

now add up the like terms:

21x+20

so we can say that f(g(x))=21x+20

which is a linear equation... and so it's domain is all real numbers :)

Answer 8

You there?

Answer 9

Yeah sorry I was working it out thank you so much!

Answer 10

np :) do you need my help with 8,9, and 10? or do you want to try them out yourself?

Answer 11

I can check your answers after your done if you want :)

Answer 12

I think ill try it out myself first but there was one on the other side i have spent so much time on and still can't get:
Solve and check for extraneous solutions: \[6x=\sqrt{24+12x}\]

Answer 13

I get confused in the factoring

Answer 14

and thank you:)

Answer 15

okay, well first off:

you can simplify the right side:
\[6x=\sqrt{4(6+3x)}\]
you can take the four out of the radical:
\[6x=2\sqrt{6+3x}\]
now divide both sides by 2:
\[3x=\sqrt{6+3x}\]
Now, you can get rid of the radical, by squaring both sides:
\[9x ^{2}=6+3x\]
Now, move everything on the right to the left (subtract both sides by 6+3x):
\[9x^2-3x-6\]
now you can factor:
\[(9x+6)(x-1)\]
Now take the (9x+6) and the (x-1) and "separate them"
set each equal to 0:

\[9x+6=0\] and \[x-1=0\]

For the first one subtract 6 from sides and divide by 9:
you get
\[x=-2/3\]

for the second one, add one to both sides:
\[x=1\]

now we can say that x=-2/3 and 1

Answer 16

hope that helps :)

Answer 17

thank you very much i am about halfway through but need to do something for 15 min with family so brb:)

Answer 18

hahah np :)

Answer 19

How do you get from the 9x to the 3x by factoring?

Answer 20

sorry not the 3x but the step after 9x^2-3x-2