SOLUTION: please help me : given that for all values x: 3x�+12x+5= p(x+q)�+r a) find the values of p,q and r

Question 233238: please help me :
given that for all values x:
3x�+12x+5= p(x+q)�+r

a) find the values of p,q and r
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
given that for all values x:
3x�+12x+5= p(x+q)�+r
a) find the values of p,q and r
----------------------
If it is true for all values of x the left side must be identical
to the right side.
----------------------
3x^2 + 12x + 5 = px^2 + 2pqx + pq^2+r
---
Equate the coefficients of corresponding terms.
p must equal 3
---
12 must equal 2pq
---
5 must equal pq^2+r
--------------------------
Solve for p,q,r
p = 3
2pq = 12; so 2*3q=12; so q = 2
-------------------
pq^2+r = 5 ;so 3*2^2+r = 5 ; so r = -7
==========================================
Cheers,
Stan H.
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