FactorSteps - Maple Help
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Student[Basics]

  

FactorSteps

  

generate steps in factoring polynomials

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

FactorSteps( expr, variable )

FactorSteps( expr, implicitmultiply = true )

Parameters

expr

-

string or expression

variable

-

(optional) variable to collect the terms by

implicitmultiply

-

(optional) truefalse

output = ...

-

(optional)

displaystyle = ...

-

(optional)

Description

• 

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.

Examples

withStudent:-Basics:

FactorStepsx3+6x2+12x+8

1. Trial EvaluationsRewrite in standard formThe factors of the constant coefficient8are:C=1,2,4,8Trial evaluations ofxin±Cfindx=−2satisfies the equation, sox+2is a factorDivide byx+2z2PPx2P+4xPP+4)x21x31+6x21+12x1+8x3+2x2.4x2+12x4x2+8x.4x+84x+8.0Quotient times divisor from long division2. Examine term:x2+4x+43. Apply the AC MethodExamine quadraticLook at the coefficients,Ax2+Bx+CA=1,B=4,C=4Find factors of |AC| = |14| =41,2,4Find pairs of the above factors, which, when multiplied equal4,Which pairs of these factors have asumof B =4? Found:=4Split the middle term to use above pairFactorxout of the first pairFactor2out of the second pairx+2is a common factorGroup common factorThis gives:4. This gives:

(1)

FactorStepsa2b2

1. This is a difference of squares, in the formA2B22. Apply difference of squares rule:A2B2=A+BAB

(2)

FactorStepsx2x12

1. Apply the AC MethodRewrite in standard formLook at the coefficients,Ax2+Bx+CA=1,B=−1,C=−12Find factors of |AC| = |1−12| =121,2,3,4,6,12Find pairs of the above factors, which, when multiplied equal12,,Which pairs of these factors have adifferenceof B =−1? Found:=−1Split the middle term to use above pairFactorxout of the first pairFactor−4out of the second pairx+3is a common factorGroup common factorThis gives:

(3)

FactorSteps2y25+113y5+33

1. Remove rationals and common factor2. Examine term:3. Apply the AC MethodExamine quadraticLook at the coefficients,Ay2+By+CA=2,B=113,C=165Find factors of |AC| = |2165| =3301,2,3,5,6,10,11,15,22,30,33,55,66,110,165,330Find pairs of the above factors, which, when multiplied equal330,,,,,,,Which pairs of these factors have asumof B =113? Found:=113Split the middle term to use above pairFactoryout of the first pairFactor55out of the second pair2y+3is a common factorGroup common factorThis gives:4. This gives:

(4)

Compatibility

• 

The Student[Basics][FactorSteps] command was introduced in Maple 2021.

• 

For more information on Maple 2021 changes, see Updates in Maple 2021.

See Also

Student:-Basics

Student:-Basics:-ExpandSteps

Student:-Basics:-LinearSolveSteps

Student:-Calculus1:-ShowSolution

Student:-Calculus1:-ShowSteps