Difference between revisions of "FactoredPolynomial1"
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<b>Setup:</b> |
<b>Setup:</b> |
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For the factored form we need to change to the <code>PolynomialFactors-Strict</code> context and restrict the allowed powers to either 0 or 1 using the <code>LimitedPowers::OnlyIntegers</code> block of code. Note: restricting all exponents to 0 or 1 means that repeated factors will have to be entered in the form <code>k(ax+b)(ax+b)</code> instead of <code>k(ax+b)^2</code>. Also, restricting all exponents to 0 or 1 means that the polynomial must factor as a product of linear factors (no irreducible quadratic factors can appear). Of course, we could allow exponents to be 0, 1, or 2, but then students would be allowed to enter <i>reducible</i> quadratic factors. There are no restrictions on the coefficients, i.e., the quadratic could have any nonzero leading coefficient. We set <code>singleFactors=>0</code> so that repeated, non-simplified factors do not generate errors. |
For the factored form we need to change to the <code>PolynomialFactors-Strict</code> context and restrict the allowed powers to either 0 or 1 using the <code>LimitedPowers::OnlyIntegers</code> block of code. Note: restricting all exponents to 0 or 1 means that repeated factors will have to be entered in the form <code>k(ax+b)(ax+b)</code> instead of <code>k(ax+b)^2</code>. Also, restricting all exponents to 0 or 1 means that the polynomial must factor as a product of linear factors (no irreducible quadratic factors can appear). Of course, we could allow exponents to be 0, 1, or 2, but then students would be allowed to enter <i>reducible</i> quadratic factors. There are no restrictions on the coefficients, i.e., the quadratic could have any nonzero leading coefficient. We set <code>singleFactors=>0</code> so that repeated, non-simplified factors do not generate errors. |
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Revision as of 14:21, 1 December 2010
Polynomial Factoring
This PG code shows how to require students to factor a polynomial.
- Download file: File:FactoredPolynomial1.txt (change the file extension from txt to pg when you save it)
- File location in NPL:
NationalProblemLibrary/FortLewis/Authoring/Templates/Algebra/FactoredPolynomial1.pg
| PG problem file | Explanation |
|---|---|
|
Problem tagging: |
|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "contextPolynomialFactors.pl", "contextLimitedPowers.pl", ); TEXT(beginproblem()); |
Initialization:
We require additional contexts provided by |
#
# Vertex form
#
Context("Numeric");
$poly = Compute("8x^2+28x+12");
#
# Factored form
#
Context("PolynomialFactors-Strict");
Context()->flags->set(singleFactors=>0);
LimitedPowers::OnlyIntegers(
minPower => 0, maxPower => 1,
message => "either 0 or 1",
);
$factored = Compute("4(2x+1)(x+3)");
|
Setup:
For the factored form we need to change to the |
Context()->texStrings;
BEGIN_TEXT
Write the quadratic expression \( $poly \)
in factored form
\( k(ax+b)(cx+d) \).
$BR
$BR
\{ ans_rule(30)\}
END_TEXT
Context()->normalStrings;
|
Main Text:
We should explicitly tell students to enter answers in the form |
$showPartialCorrectAnswers = 1; ANS( $factored->cmp() ); |
Answer Evaluation: Everything is as expected. |
Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;
COMMENT('MathObject version.');
ENDDOCUMENT();
|
Solution: |
