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Wed Oct 19 17:03:53 2005 UTC (7 years, 7 months ago) by jj
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    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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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