generate steps in factoring polynomials
Student[Basics][FactorSteps]( expr, variable )
Student[Basics][FactorSteps]( expr, implicitmultiply = true )
string or expression
(optional) variable to collect the terms by
output = ...
displaystyle = ...
The FactorSteps command accepts a polynomial and displays the steps required to factor the expression.
If expr is a string, then it is parsed into an expression using InertForm:-Parse so that no automatic simplifications are applied, and thus no steps are missed.
The implicitmultiply option is only relevant when expr is a string. This option is passed directly on to the InertForm:-Parse command and will cause things like 2x to be interpreted as 2*x, but also, xyz to be interpreted as x*y*z.
The output and displaystyle options are described in Student:-Basics:-OutputStepsRecord. The return value is controlled by the output option.
This function is part of the Student[Basics] package, so it can be used in the short form FactorSteps(..) only after executing the command with(Student[Basics]). However, it can always be accessed through the long form of the command by using Student[Basics][FactorSteps](..).
▫1. Trial Evaluations◦Rewrite in standard form◦The factors of the constant coefficient8are:C=1,2,4,8◦Trial evaluations ofxin±Cfindx=−2satisfies the equation, sox+2is a factor◦Divide byx+2x22x2+4⁢x+4)x21x31+6⁢x21+12⁢x1+8x3+2⁢x2.4⁢x2+12⁢x4⁢x2+8⁢x.4⁢x+84⁢x+8.0◦Quotient times divisor from long division•2. Examine term:x2+4⁢x+4▫3. Apply the AC Method◦Examine quadratic◦Look at the coefficients,A⁢x2+B⁢x+CA=1,B=4,C=4◦Find factors of |AC| = || =41,2,4◦Find pairs of the above factors, which, when multiplied equal4,◦Which pairs of these factors have asumof B =4? Found:=4◦Split the middle term to use above pair◦Factorxout of the first pair◦Factor2out of the second pair◦x+2is a common factor◦Group common factorThis gives:•4. This gives:
•1. Difference of squares
▫1. Apply the AC Method◦Rewrite in standard form◦Look at the coefficients,A⁢x2+B⁢x+CA=1,B=−1,C=−12◦Find factors of |AC| = || =121,2,3,4,6,12◦Find pairs of the above factors, which, when multiplied equal12,,◦Which pairs of these factors have adifferenceof B =−1? Found:=−1◦Split the middle term to use above pair◦Factorxout of the first pair◦Factor−4out of the second pair◦x+3is a common factor◦Group common factorThis gives:
•1. Remove rationals and common factor•2. Examine term:▫3. Apply the AC Method◦Examine quadratic◦Look at the coefficients,A⁢y2+B⁢y+CA=2,B=113,C=165◦Find factors of |AC| = || =3301,2,3,5,6,10,11,15,22,30,33,55,66,110,165,330◦Find pairs of the above factors, which, when multiplied equal330,,,,,,,◦Which pairs of these factors have asumof B =113? Found:=113◦Split the middle term to use above pair◦Factoryout of the first pair◦Factor55out of the second pair◦2⁢y+3is a common factor◦Group common factorThis gives:•4. This gives:
The Student[Basics][FactorSteps] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
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