View of /trunk/NationalProblemLibrary/maCalcDB/setAlgebra04ExpressionsFactoring/factor_hard5.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('factoring', 'identities')
    3 ## hcao tagged and PAID on 2-20-2004
    4 
    5 ## DBsubject('Algebra')
    6 ## DBchapter('Basic Algebra')
    7 ## DBsection('Algebraic Expressions')
    8 ## Date('6/3/2002')
    9 ## Author('')
   10 ## Institution('')
   11 ## TitleText1('College Algebra')
   12 ## EditionText1('3')
   13 ## AuthorText1('Stewart, Redlin, Watson')
   14 ## Section1('1.4')
   15 ## Problem1('67 78')
   16 ##DIFFICULTY('hard')
   17 ##  Choose the method of factorization
   18 ##ENDDESCRIPTION
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl",
   28 );
   29 
   30 $showPartialCorrectAnswers = 1;
   31 
   32 TEXT(&beginproblem);
   33 
   34 $A = random(1,9,1);
   35 $B = non_zero_random(-8,8,1);
   36 while (gcd($A,$B) > 1 || $B==-$A) {$B = random(1,9,1);}
   37 
   38 $C = random(1, 9,1);
   39 
   40 $c1 = $A**2;
   41 $c2 = 2*$A*$B;
   42 $c3 = $B**2;
   43 $c4 = -$C**2;
   44 
   45 $e = random(2,7,1);
   46 $e2 = 2*$e;
   47 
   48 $E = non_zero_random(-8,8,2);
   49 
   50 BEGIN_TEXT
   51 
   52 The polynomial \($c1 a^{$e2} + $c2 a^{$e}b + $c3 b^2 + $c4 c^{$E}\)
   53 can be factored into
   54 the product of two polynomials, \(A \cdot B \)
   55 where the coefficient of \(c\) in \(A\) is
   56 less than the coefficient of \(c\) in \(B\).  Find \(A\) and \(B\).
   57 $BR
   58 $BR
   59 \(A = \) \{ans_rule(10)\}
   60 $BR
   61 \(B = \) \{ans_rule(10)\}
   62 END_TEXT
   63 
   64 $ans1 = "$A*a**$e+$B*b-$C*c**($E/2)";
   65 $ans2 = "$A*a**$e+$B*b+$C*c**($E/2)";
   66 
   67 &ANS(fun_cmp ($ans1, var=>['a','b','c']));
   68 &ANS(fun_cmp ($ans2, var=>['a','b','c']));
   69 ENDDOCUMENT();        # This should be the last executable line in the problem.;
   70