ExpandedPolynomial1

Polynomial Multiplication (Expanding)

This PG code shows how to require students to expand polynomial multiplication.

• Download file: File:ExpandedPolynomial1.txt (change the file extension from txt to pg when you save it)
• File location in NPL: NationalProblemLibrary/FortLewis/Authoring/Templates/Algebra/ExpandedPolynomial1.pg

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "contextLimitedPolynomial.pl", ); TEXT(beginproblem());	Initialization: We must load contextLimitedPolynomial.pl
# # Vertex form # Context("Numeric"); $h = 3; $k = 5; $vertexform = Compute("(x-$h)^2-$k"); # # Expanded form # Context("LimitedPolynomial-Strict"); $b = -2 * $h; $c = $h**2 - $k; $expandedform = Formula("x^2 + $b x + $c")->reduce();	Setup: The macro contextLimitedPolynomial.pl provides two contexts: Context("LimitedPolynomial"); Context("LimitedPolynomial-Strict"); The strict version does not allow any mathematical operations within coefficients, so (5+3)x must be simplified to 8x. For more details, see contextLimitedPolynomial.pl.html We use the LimitedPolynomial-Strict context, construct the coefficients $b and $c as Perl reals, and then construct $expandedform using these pre-computed coefficients. This is because the LimitedPolynomial-Strict context balks at answers that are not already simplified completely. Notice that we called the ->reduce() method on the expanded form of the polynomial, which will ensure that the polynomial will be displayed as x^2 - 6x + 4 instead of x^2 + -6x + 4.
Context()->texStrings; BEGIN_TEXT The quadratic expression \( $vertexform \) is written in vertex form. Write the expression in expanded form \( ax^2 + bx + c \). $BR $BR \{ ans_rule(30) \} END_TEXT Context()->normalStrings;	Main Text: To help students understand how to format their answers, we give an example ax^2+bx+c of what the answer should look like.
$showPartialCorrectAnswers = 1; ANS( $expandedform->cmp() );	Answer Evaluation:
Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();	Solution:

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