Question

⇒ s′(t)=4(2t−3)(8−2t)^3−6(2t−3)^2(8−2t)^2
how can i factor this? I keep factoring incorrectly :(

Answer 1

Show me what you have done.

Answer 2

How many (2t-3) can you pull out?

Answer 3

I used 2 to factor since it goes in both 4 and -6

Answer 4

1

Answer 5

ok so that is part of it

Answer 6

\[4(2t-3)(8-2t)^{3}-6(2t-3)^{2}(8-2t)^{2}\]
\[(2t-3)(8-2t)^{2}[4(8-2t)-6(2t-3)]\]

I'll stop here as to not go all the way, but maybe you can see what I was doing?

Answer 7

The problem is im not sure how to factor these anymore. i did a similar problem like this.. only they factored out an outer number and here: we factor one of the insides number. im so confused.

Answer 8

Do you follow what @psymon did?

Answer 9

yes but why can't we pull out a 2 in the outside since it' can go into 4 and -6?

Answer 10

ok I have dealt with this before ... it is tough to see. There really are only 2 terms in your original equation...do you see that?

Answer 11

Because I rather not do too much at once and worry about mistakes.

Answer 12

and no i didn't follow... this is where im stuck

Answer 13

But Psymon could have done that too.

Answer 14

yes i see

Answer 15

Look you actually only have two terms with several factors each. Hang on..

Answer 16

The first term is 4(2t-3)(8-2t)^3

Answer 17

That is one big term because it is composed of things being multiplied together (called factors)

Answer 18

ok

Answer 19

the factors of the first term are 4, (2t-3), and (8-2t)

Answer 20

right

Answer 21

So what would be the 2nd term? @mathcalculus

Answer 22

-6, (2t-3) and (8-2t)

Answer 23

@Paynesdad

Answer 24

Good so now think of factoring something easy... like 6x^2-15x ... you factor out the common factors and leave whatever is left ... right?

Answer 25

yes

Answer 26

In other words you factor out 3 and x and leave (2x-5) right?

Answer 27

correct

Answer 28

So now look at your equation ... what things and how many can you factor out of both terms

Answer 29

thats what i was saying... 2 goes in for 4 and -6..

Answer 30

Ok what other factors can you factor out?

Answer 31

i can factor (2t-3) and (8-2t)

Answer 32

Right how many 2t-3 can you factor out remember you can only factor out as many as the least number in either of the two terms.

Answer 33

1

Answer 34

right and how many 8-2t?

Answer 35

@Paynesdad right i know i can factor that too but what about the outer numbers. should i factor that firsT?

Answer 36

2

Answer 37

you can it shouldn't matter.

Answer 38

so factor out 2(2t-3)(8-2t)^2 and show me what you are left with

Answer 39

yes it does.... for ex::

Answer 40

see they factored out using the 4

Answer 41

That doesn't dispute what I was saying it doesn't matter if you factor out the 2 right now or not.

Answer 42

This is just how I might go about doing these on paper. Looks like you're getting closer to understanding though, @mathcalculus ^_^