Flashcards
Polynomial Factorization Flash Cards
Cards in this deck (17)
- 1Difference of Two Squares (Generic) Binomial( a^2 - b^2 )
= ( a + b ) * ( a - b ) - 2Difference of Two Squares (Factor) 9x^2 - 25y^2 Binomial( 3x + 5y ) * ( 3x - 5y )
- 3Difference of Two Squares (Factor) ( a + b )^2 - 25 Binomial= [ ( a + b ) + 5 ] * [ ( a +b ) - 5 ]
= ( a + b + 5 ) * ( a + b - 5 ) - 4Sum of Two Squares BinomialDoes Not Factor, The Polynomial is Prime
- 5Sum of Two Cubes (Generic) Binomiala^3 + b^3
= ( a + b ) * ( a^2 - ab + b^2)
*Resulting Trinomials Don't Factor Further* - 6Sum of Two Cubes (Factor) 8x^3 + 27y^3 Binomial( 2x + 3y ) * ( 4x^2 - 6xy + 9y^2)
*Resulting Trinomials Don't Factor Further* - 7Difference of Two Cubes (Generic) Binomiala^3 - b^3
= ( a - b ) * ( a^2 + ab + b^2 )
*Resulting Trinomials Don't Factor Further* - 8Difference of Two Cubes (Factor) x^3 - 64 Binomial( x - 4 ) * ( x^2 + 4x + 16 )
*Resulting Trinomials Don't Factor Further* - 9Square of a Binomial (Generic) Trinomiala^2 + 2ab + b^2
= ( a + b ) * ( a + b ) = ( a + b )^2 - 10Square of a Binomial (Factor) x^2 + 6x + 9 Trinomial( x + 3 ) * ( x + 3 )
= ( x + 3 )^2 - 11Square of a Binomial (Factor) 4x^2 - 20xy + 25y^2 Trinomial( 2x - 5y ) * ( 2x - 5y )
= ( 2x -5y )^2 - 12If a = 1, what are you supposed to do? ( a^2 + 2ab + b^2 )Reverse Foil
- Last
- Inner
- Outer
- First
Or use trial and error - 13If a ≠ 1, what are you supposed to do? ( a^2 + 2ab + b^2 )Use the trial and error method
( Grouping may also be needed ) - 14Group the first and last two terms 5a - 5b - xa + xb (4 Terms)= ( 5a - 5b ) + ( -xa + xb )
= 5 * ( a - b ) - x * ( a - b )
= ( a - b ) * ( 5 - x ) - 15Group the first and last two terms x^3 - 3x^2 + 2x - 6 (4 Terms)= ( x^3 - 3x^2 ) + ( 2x - 6 )
= x^2 * ( x - 3 ) + 2 * ( x - 3 )
= ( x - 3 ) * ( x^2 + 2 ) - 16Group the first three terms x^2 + 6x + 9 - y^2 (4 Terms)= ( x^2 + 6x + 9 ) - y^2
= ( x + 3 )^2 - y^2
= [ ( x + 3 ) + y ] * [ ( x + 3 ) - y ]
= ( x + 3 + y ) * ( x + 3 - y ) - 17Group the last three terms y^2 - x^2 + 6x - 9 (4 Terms)= y^2 - ( x^2 - 6x + 9 )
= y^2 - ( x - 3 )^2
= [ y + ( x - 3 ) ] * [ y - ( x - 3 ) ]
= ( y + x - 3 ) * ( x + x + 3 )
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- Description
- A set of flash cards designed to help remember the formulas of specified factoring principles.
- Created by
- Jeremy Bailey
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