View of /trunk/NationalProblemLibrary/maCalcDB/setAlgebra04ExpressionsFactoring/Test1_17.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')
   16 ##DIFFICULTY('hard')
   17 ##  Factoring a perfect square trinomial with 2 variables
   18 ##
   19 ## Author:  Mark Schmitt
   20 ## Date:    2001/02 School Year
   21 ## Course:  Algebra 2 (Honors or Regular)
   22 ##
   23 ##ENDDESCRIPTION
   24 
   25 DOCUMENT();        # This should be the first executable line in the problem.
   26 
   27 loadMacros(
   28 "PG.pl",
   29 "PGbasicmacros.pl",
   30 "PGchoicemacros.pl",
   31 "PGanswermacros.pl",
   32 "PGauxiliaryFunctions.pl",
   33 );
   34 
   35 $showPartialCorrectAnswers = 1;
   36 
   37 TEXT(&beginproblem);
   38 
   39 $A = random(1,9,1);
   40 $B = non_zero_random(-9,9,1);
   41 while (gcd($A,$B) > 1) {$B = random(1,9,1);}
   42 
   43 $C = random(1,9,1);
   44 $D = random(1,9,1);
   45 while (gcd($C,$D)>1) {$D = random(1,9,1);}
   46 
   47 $c1 = $A**2;
   48 $c2 = $B**2;
   49 $e1 = $C*2;
   50 $e2 = $D*2;
   51 $c3 = 2*$A*$B;
   52 
   53 BEGIN_TEXT
   54 
   55 The polynomial \($c1 x^{$e1} +$c3 x^{$C} y^{$D} + $c2 y^{$e2} \)
   56 can be factored into
   57 the product of two polynomials, \(A \cdot B\) where the
   58 coefficient of y in \(A\) is
   59 greater than or equal to the coefficient of y in \(B\).  Find \(A\) and \(B\).
   60 $BR
   61 $BR
   62 \(A = \) \{ans_rule(10)\}
   63 $BR
   64 \(B = \) \{ans_rule(10)\}
   65 
   66 END_TEXT
   67 
   68 $ans1 = "$A*x**$C + $B*y**$D";
   69 $ans2 = "$A*x**$C + $B*y**$D";
   70 
   71 &ANS(fun_cmp ($ans1,var=>['x','y']));
   72 &ANS(fun_cmp ($ans2,var=>['x','y']));
   73 
   74 ENDDOCUMENT();        # This should be the last executable line in the problem.;
   75