Expanded Polynomial

This problem gives the student a quadratic in factored form and asks for the equivalent in expanded/general form.

Complete Code

POD for Macro Files

contextLimitedPolynomial.pl

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',               'PGML.pl',
    'contextLimitedPolynomial.pl', 'PGcourse.pl'
);

Preamble

We must load contextLimitedPolynomial.pl

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.

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.

BEGIN_PGML
The quadratic expression [`[$vertexform]`] is written in vertex form.
Write the expression in expanded form [`ax^2 + bx + c`].

[_]{$expandedform}{20}
END_PGML

Statement

To help students understand how to format their answers, we give an example ax^2+bx+c of what the answer should look like.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.