Yet another factoring problem (1 Viewer)

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

I asked my friends about this and they were stumped too.

(a^2-5a)^2 + 8(a^2-5a)+12

Since it's a trinomial, I tried to do decomposition but it didn't work. I tried to factor out the (a^2-5a) but I end up with a different answer then on the sheet.
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,848
128
Set y=a^2-5a.
Factorize your expresion in terms of y first
 
so would it be ax^2+bx+c=0?
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,848
128
x presumably meaning y, yes, you'll see how to factorize the polynomial once you've found the roots of your cited equation, with the relevant values for "a,b,c"
("a" NOT meaning the same here as above).
 
would it be 1,8 and 12?
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,848
128
That is correct.
 
But where do I go from there? My friendsa nd I are stumped. Our teacher never taught us this >_>
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,848
128
What are the roots of the equation:
[tex]y^{2}+8*y+12=0[/tex]?
How can you therefore factorize the polynomial [itex]y^{2}+8y+12[/itex]?
 
(y+4)(y+3)=0
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,848
128
No. Try again.
 
err whoops
(y+2)(y+6)=0
 
I got the decomposition mixed up (which term to add up and which to multiply)
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,848
128
So, you've factorized the left hand side of your EQUATION correctly.
How is thereby the POLYNOMIAL [itex]y^{2}+8y+12[/itex] factorized?
 
I'm not sure what you are asking for, I thought I just factored the polynomial
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,848
128
OK:
For ANY number y, we have the identity [itex]y^{2}+8y+12=(y+2)(y+6)[/tex]
This is to factorize the POLYNOMIAL.


The two numbers -2 and -6 are the solutions Y for the equation [itex]Y^{2}+8Y+12=0[/itex]

Do you agree with that?
 
Right, I understand that part. (Sorry if I'm a bit slow)
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,848
128
That's okay.
Now that you've factorized your polynomial in y, substitute into its factorized form (y+2)(y+6) on the y-places y=a^2-5a.
What do you get then?
In particular, can you do some further factorizations?
 
so would it be (a^2-5a)(a+2)(a+6)?
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,848
128
Eeh, why??
Have you placed the expression a^2-5a into the y-places correctly, do you think?
 
OH....is it...(a^2-5a)(a-2)(a-3)?
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top