Factored polynomial
Download file: SimpleFactoring.pg
DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');
Preamble
These standard macros need to be loaded.($x0, $x1) = (non_zero_random(-6, 6), non_zero_random(-6, 6));
$factor1 = Compute("x-$x0")->reduce;
$factor2 = Compute("x-$x1")->reduce;
$f = Compute("x^2-($x0+$x1)x+$x0*$x1")->reduce;
$factors = List($factor1, $factor2);
$roots = List($x0, $x1);
# If there were only one solution
# $roots = List(4);
# If there were no solutions
# $roots = List("NONE");
Setup
First, we create two random roots and then create the factors. Note: the ->reduce will help make x-(-3) into x+3. In addition, we create the expanded form of the quadratic.
Note that the argument of the List call are the objects in the list, which can be any MathObjects. Here we create a list of Formulas and a list of Reals (the numbers that we use in the second list will be promoted to Real MathObjects when the List is created).
If, for example, there were no real roots, we should set $roots = List("NONE"); so that students who enter a list of roots will not receive an error message about entering the wrong type of answer. If we were to use $roots = String("NONE"); instead, students who enter anything other than a string (e.g., a list of numbers) will receive an error message.
Similarly, if there were only one root at x=4, we would use $roots = List(4); instead of $roots = Real(4); to avoid sending error messages to students who enter multiple answers or NONE.
BEGIN_PGML
a) What are the factors of [`[$f]`]?
Factors = [__]{$factors}
b) What are the roots of this equation?
Roots = [__]{$roots}
_(Enter both answers as a comma-separated list.)_
END_PGML
Statement
This is the problem statement in PGML.BEGIN_PGML_SOLUTION Solution explanation goes here. END_PGML_SOLUTION ENDDOCUMENT();
Solution
A solution should be provided here.