<PRE><B>Question 233238</B>
given that for all values x:
3x²+12x+5= p(x+q)²+r

a) find the values of p,q and r 
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If it is true for all values of x the left side must be identical 
to the right side.
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3x^2 + 12x + 5 = px^2 + 2pqx + pq^2+r
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Equate the coefficients of corresponding terms.
p must equal 3
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12 must equal 2pq
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5 must equal pq^2+r
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Solve for p,q,r
p = 3
2pq = 12; so 2*3q=12; so q = 2
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pq^2+r = 5 ;so 3*2^2+r = 5 ; so r = -7
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Cheers,
Stan H.</PRE>