Factored Polynomial

Factored polynomial

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',               'PGML.pl',
    'contextPolynomialFactors.pl', 'contextLimitedPowers.pl',
    'PGcourse.pl'
);

Preamble

We require additional contexts provided by contextPolynomialFactors.pl and contextLimitedPowers.pl

# Expanded 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 PolynomialFactors-Strict context and restrict the allowed powers to either 0 or 1 using the LimitedPowers::OnlyIntegers block of code. Note: restricting all exponents to 0 or 1 means that repeated factors will have to be entered in the form k(ax+b)(ax+b) instead of k(ax+b)^2. 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 reducible quadratic factors. There are no restrictions on the coefficients, i.e., the quadratic could have any nonzero leading coefficient. We set singleFactors => 0 so that repeated, non-simplified factors do not generate errors.

BEGIN_PGML
Write the quadratic expression [`[$poly]`] in factored form [`k(ax+b)(cx+d)`].

[_]{$factored}{20}
END_PGML

Statement

We should explicitly tell students to enter answers in the form k(ax+b)(cx+d).

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.