Problem Factoring Functions...

[eric_f]

Hi All,

I am able to complete this problem, but I'd like some assistance in the factoring department. I know what the factors should be, but get lost on the way there.

Attached is the question from the book. It's an even numbered one so no help from the solution guide.



h(t)=25t - 4.9t^2
h(1)=25 - 4.9

so:

(25t - 4.9t^2) - (25 - 4.9)

rearranging, I get:

(25t - 25) - (4.9t^2 - 4.9)

Factor out:

25(t - 1) - 4.9(t^2 - 1)

25(t - 1) - 4.9(t + 1)(t - 1)

And here is where I get stuck... It's probably something painfully obvious, but I don't see how I'd end up at (t - 1)(20.1 - 4.9t).

This is the answer I was given from another source, but he lost me at the same step...

25t - 25 - 4.9t^2 - 4.9
= 25(t - 1 ) - 4.9 (t^2 - 1 )
= 25 ( t - 1 ) - 4.9 ( t +1 ) ( t - 1 )
(get lost here)
= (t - 1 ) [ 25 - 4.9 ( t + 1 ) ]
= ( t - 1 ) ( - 4.9t + 20.1 )

Thanks for any insight! It's probably something painfully obvious


~Eric

 

[MarkFL]

Hello Eric,

Let's take it from the point at which you are stuck:

\(\displaystyle 25(t-1)-4.9(t+1)(t-1)\)

Now, notice that both terms have \(\displaystyle t-1\) as a factor, so pull that out front:

\(\displaystyle (t-1)(25-4.9(t+1))\)

Now distribute the -4.9...

\(\displaystyle (t-1)(25-4.9t-4.9)\)

Combine like terms:

\(\displaystyle (t-1)(20.1-4.9t)\)

 

[Bob Brown MSEE]

25(t - 1) - 4.9(t + 1)(t - 1)

And here is where I get stuck... It's probably something painfully obvious, but I don't see how I'd end up at (t - 1)(20.1 - 4.9t).

25(t - 1) - 4.9(t + 1)(t - 1)
(t - 1)(25- 4.9(t + 1))
(t - 1)(25- 4.9t - 4.9)
(t - 1)(20.1- 4.9t)

 

[wjm11]

Hi All,

I am able to complete this problem, but I'd like some assistance in the factoring department. I know what the factors should be, but get lost on the way there.

Attached is the question from the book. It's an even numbered one so no help from the solution guide.

View attachment 2789

h(t)=25t - 4.9t^2
h(1)=25 - 4.9

so:

(25t - 4.9t^2) - (25 - 4.9)

rearranging, I get:

(25t - 25) - (4.9t^2 - 4.9)

Factor out:

25(t - 1) - 4.9(t^2 - 1)

25(t - 1) - 4.9(t + 1)(t - 1)

And here is where I get stuck... It's probably something painfully obvious, but I don't see how I'd end up at (t - 1)(20.1 - 4.9t).

This is the answer I was given from another source, but he lost me at the same step...

25t - 25 - 4.9t^2 - 4.9
= 25(t - 1 ) - 4.9 (t^2 - 1 )
= 25 ( t - 1 ) - 4.9 ( t +1 ) ( t - 1 )
(get lost here)
= (t - 1 ) [ 25 - 4.9 ( t + 1 ) ]
= ( t - 1 ) ( - 4.9t + 20.1 )

Thanks for any insight! It's probably something painfully obvious


~Eric

If it is just the single factoring step you need help with, here is what is going on:
The expression " 25 ( t - 1 ) - 4.9 ( t +1 ) ( t - 1 ) " has two separate terms.
Term 1: 25 ( t - 1 ) )
Term 2: - 4.9 ( t +1 ) ( t - 1 )
They share a common factor, namely (t-1).
When we factor this term out of the two terms, we get: (t - 1 ) [ 25 - 4.9 ( t + 1 ) ]

Hope that helps.

Edit: Oops. For some reason I did not see the other responses initially.

 

[eric_f]

Well, now it makes sense; I can't believe I missed that! Thanks for the nudge in the right direction, I'm sure I'll be back for more.

~Eric