Linear Factors of 2x^2-x-6

J

John Whitaker

Junior Member
Joined
May 9, 2006
Messages
89
I can't find (in my books) how to isolate the Linear Factors of an expression 2x^2-x-6. I would like to have the procedure explained. Thank you. John
 
John, I did not answer earlier because I wanted to see what others would do.
As usual, Eliz has come through splendidly.

I will now post my take.
If you really want to learn the process, go and multiply out say 100-200 binomials.
Like: (x-3)(x+2), (2x-1)(3x+2), (x-6)(x-1) etc.
That is simply the way to learn it.
 
Thank you. Not looking for a course. I've factored quardatic trinomials with no problems, but I am being thrown off by the word "linear." The only definition I can find states the variable has only the power of 1. I imagine there is more to this definition.
My book says that 2x+3 is a "linear factor" of 2x^2-x-6 and I can't see how that answer is developed. I was hoping to see the process regarding this one expression. If this is outside the rules, sorry. Thanks anyway. John
 
Since the leading coefficient is not 1, it makes it a little trickier, but not much.

Find 2 numbers which when multiplied equals -12 and when added equals
-1.

-1 is the coefficient of x and -12 is 2 times the constant(because of the 2 in the lead).

How about -4 and 3. (-4)(3)=-12, -4+3=-1

\(\displaystyle 2x^{2}-4x+3x-6\)

\(\displaystyle (2x^{2}-4x)+(3x-6)\)

Factor:

\(\displaystyle 2x(x-2)+3(x-2)\)

\(\displaystyle \L\\(2x+3)(x-2)\)
 
One never knows what is really being call for.
In my first year of university teaching, in PreCalculus class a student had a question about a problem. After reading it, something told me to ask her about the problem. She said “Well I don’t know what that word means.” The word was ‘circumference’. I ask her if she had looked it up in a dictionary. Her response “Would that in a dictionary?”
 
John Whitaker said:
I can't find (in my books) how to isolate the Linear Factors of an expression 2x^2-x-6. I would like to have the procedure explained. Thank you. John
Click to expand...

"isolate the Linear Factors of 2x^2 - x - 6"
is simply another way of saying:
"factor 2x^2 - x - 6"
...and that's: (x - 2)(2x + 3)

To use "isolate the Linear Factors of" instead of simply "factor" is as annoying to me as
using "at this point in time" instead of simply "now" :evil:
 
I substantially agree with you, but if the section in the book has just stressed the concept of "degree", it may be a bit more justifiable.
 
Perhaps the writer of the book was paid by the word. Thank you all. I appreciate all your help. John
 
You must log in or register to reply here.
Top