Simplyfying (Indentitied related)

  • #1
ASMATHSHELPME
10
0
Simple for you guys i guess, But tough for me - Guess I am just thick!

[itex]x^4 +Ax^3 + 5x^2 + x + 3 = (x^2 +4)(X^2 -x +B) +Cx +D[/itex]

I get:

[itex]x^4 +Ax^3 + 5x^2 + x + 3 = X^4 -x^3 - 4x^2 + Bx^2 - 4x + 4B + Cx + D[/itex]

Now, I think i need to simplify this more because i can't compare co-efficients can i?

Can someone run me through the further simplifications?

Maybe [itex]Bx^2 + 4x^2[/itex] into [itex](4+B)X^2[/itex] ? Is this wise and possible? What else?

Need to learn simplification better, Finding my basic maths is poor so Alevel is tough!
 

Answers and Replies

  • #2
hypermorphism
506
1
The law of distribution of multiplication over addition: a*(b + c) = a*b + a*c. The equality sign means that any expression of the form of the right hand side may be replaced by the expression on the left hand side (and vice versa) and still maintain the truth of the original expression. As long as X=x in your expression, what you're doing is fine. :smile:
 
  • #3
iNCREDiBLE
128
0
You're on the right path, my friend!

[tex]x^4 +Ax^3 + 5x^2 + x + 3 = (x^2 +4)(x^2 -x +B) +Cx +D[/tex]
<=>
[tex]x^4 +Ax^3 + 5x^2 + x + 3 = x^4 - x^3 + Bx^2 + 4x^2 - 4x + 4B +Cx +D[/tex]
<=(cancellation & simplification)=>
[tex]Ax^3 + 5x^2 + x + 3 = - x^3 + (B+4)x^2 + (C-4)x + 4B + D[/tex]
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
43,021
970
Now recall that if that is true for all x, then the corresponding coefficients must be equal. You can just look at that and see what A must be!
 

Suggested for: Simplyfying (Indentitied related)

Replies
1
Views
572
Replies
2
Views
393
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
356
  • Last Post
Replies
4
Views
664
Replies
3
Views
389
  • Last Post
Replies
1
Views
436
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
8
Views
1K
Top