[npl] / trunk / NationalProblemLibrary / maCalcDB / setAlgebra04ExpressionsFactoring / Test1_17.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/maCalcDB/setAlgebra04ExpressionsFactoring/Test1_17.pg

Wed Oct 19 17:03:53 2005 UTC (7 years, 7 months ago) by jj
File size: 1626 byte(s)
Added subject tag.


    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
28 "PG.pl",
29 "PGbasicmacros.pl",
30 "PGchoicemacros.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