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

Load the contextLimitedPolynomial.pl macro.

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 contextLimitedPolynomial.pl macro 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.

Switch to the LimitedPolynomial-Strict context, construct the coefficients $b and $c, and then construct $expandedform using these coefficients. Note that the coefficients must be provided as simplified numeric values because the LimitedPolynomial-Strict context will not accept answers that are not already simplified completely. That is done here by computing those values in Perl before using them in the formula definition. Notice that the reduce method is called for the expanded form of the polynomial, which ensures 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

The example form ax^2+bx+c for the answer is given to help students understand how to format their answers.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.