Question

Factor 7(x − 3)2 − 4(x − 3) − 3 completely.

Answer 1

any ideas?

Answer 2

@mathstudent55 @zepdrix @uri

Answer 3

@sleepyjess

Answer 4

@StudyGurl14

Answer 5

@Jaynator495 @just_one_last_goodbye

Answer 6

@tanya123 @ikram002p

Answer 7

Hey :)

Answer 8

zep do you know this?

Answer 9

\[\large\rm 7(x − 3)^2 − 4(x − 3) − 3\]Is the -3 supposed to be an exponent as well?

Answer 10

i have a few of these to do... but im just starting with this one.

Answer 11

mmm no i dont believe so

Answer 12

Let's write it like this\[\large\rm =7(x-3)(x − 3) − 4(x − 3) − 3\]

Answer 13

Notice that the first and second terms have something in common,\[\large\rm =7(x-3)\color{orangered}{(x − 3)} − 4\color{orangered}{(x − 3)} − 3\]

Answer 14

yes

Answer 15

so do i cancel them?

Answer 16

=7(x - 3) - 4 - 3? if canceling like terms correct.

Answer 17

Maybe we should put some brackets here, just to prepare ourselves for what we'll do next,\[\large\rm =\left[7(x-3)\color{orangered}{(x − 3)} − 4\color{orangered}{(x − 3)}\right] − 3\]
So we divide out this common factor, and leave it as multiplication on the outside like this.\[\large\rm =\color{orangered}{(x − 3)}\left[7(x-3) − 4\right] − 3\]

Yes, you have the right idea :) Divide (x-3) out of each term,
but you can't just divide willy nilly.

To keep things balanced, you have to also multiply at the same time.
So we're dividing an (x-3) out of both terms, and saving the multiplication on the outside.

If that's too confusing, we can do a more simple example.

Answer 18

no, no I see your point. However I am confused as to which i multiply?

Answer 19

@zepdrix

Answer 20

You only multiply (x-3) by the terms which you took an (x-3) from.
So notice that we didn't include the -3 in the square brackets.
We didn't "factor" an (x-3) out of that,
so we don't want him to be included in the multiplication.
\[\large\rm =(x − 3)\left[7(x-3) − 4− 3\right]\qquad\qquad \color{red}{X}\]\[\large\rm =(x − 3)\left[7(x-3) − 4\right] − 3\qquad\qquad \color{green}{\checkmark}\]

Answer 21

Is that what your question was about? :o
Maybe I misunderstood.

Answer 22

ok so what shall i d next?

Answer 23

Hmm, I guess you could simplify the stuff that's inside of the square brackets.
\[\large\rm =(x − 3)\left[\color{royalblue}{7(x-3) − 4}\right] − 3\]

Answer 24

ok so to simplify what must be done? just multiply divide? or do i factor?

Answer 25

oh i see your point? multiply the 7 by whats in the brackets?

Answer 26

Ya distribute the 7 :) that's a good idea

Answer 27

hmm so I see 7x - 21) - 28?

Answer 28

Woops!
Notice that the 7 is only multiplying the (x-3), not the -4.

Answer 29

so 7x - 21? or is it 21x?

Answer 30

You give a 7 to the x, and a 7 to the -3.
So 7x and -21, yes.

\[\large\rm =(x − 3)\left[\color{royalblue}{7x-21 − 4}\right] − 3\]

Answer 31

sorry internet issues...

Answer 32

so now what? 21 - 4? then (7x - 17) is left right?

Answer 33

Woops!
They're both negative, so you end up with a number which is more negative.

Answer 34

-21 and go 4 more negative.

Answer 35

uh so -25?

Answer 36

\[\large\rm =(x − 3)\left[\color{royalblue}{7x-25}\right] − 3\]K cool.
We can change those back to round brackets at this point if you want.\[\large\rm =(x − 3)\left(7x-25\right) − 3\]
There is no difference in bracket, it was just so we wouldn't have a (( situation :)
Easier to read, I think.

I guess we can't do much to it besides all of that. :o

Answer 37

so more distributing?

Answer 38

No, nothing more.
That's all the factoring we can do :)

Distributing would be going the other direction.

Answer 39

uh ok

Answer 40

can i make a new tab this is starting to have connection issues.

Answer 41

@zepdrix i will make new tab and update you.

Answer 42

k :)