# Shared Flashcard Set

## Details

Factoring
Basic Concepts of Algebra-R4
10
Mathematics
03/21/2008

## Additional Mathematics Flashcards

Term
 Terms with Common Factors
Definition
 When factoring, we always try to factor out the largest factor common to all term in the polynomial, using the distributive property.e.g., 15 + 10x - 5x2 = 5(3 + 2x - x2)
Term
 Factoring by Grouping
Definition
 In some polynomials, pairs of terms have a common binomial factor that can be removed in a process called factoring by grouping.x3 + 3x2 - 5x - 15 =  (x3 + 3x2) + (-5x - 15)                                                   = x2(x + 3) - 5(x + 3)                                                   = (x + 3) (x2 - 5)
Term
 Trinomials of the Type x2 + bx + c
Definition
 To factor a trinomial of the type x2 + bx + c, we look for binomial factors of the type (x + p) (x + q), where p · q = c and p + q = b.
Term
 Trinomials of the Type ax2 + bx + c, a ≠ 1
Definition
 If poss., factor out the largest common factor.Multiply the leading coefficient and the constant.Try to factor so that the sum of the factors is the coefficent of the middle term.Split the middle term using the numbers found in step 3.Factor by grouping.12x3 + 10x2 - 8x  1.  2x(6x2 +5x -4)              2.  6(-4) = -24                     3.  -3 · 8 = -24; -3 + 8 = 5   4.  5x = -3x + 8x                5.  6x2 - 3x + 8x - 4           3x(2x -1) + 4(2x -1)(2x -1) (3x + 4)
Term
 Special Factorizations:Trinomial Squares
Definition
 A2 + 2AB + B2 = (A + B)2 A2 - 2AB + B2 = (A - B)2
Term
 Special Factorizations:Sum of Cubes
Definition
 A3 + B3 = (A + B) (A2 - AB + B2)
Term
 Special Factorizations: Difference of Cubes
Definition
 A3 - B3 = (A - B) (A2 + AB + B2)
Term
 Special Factorizations:Difference of Squares
Definition
 A2 - B2 = (A + B) (A - B)
Term
 Special Factorizations:Sum of Squares
Definition
 A2 + B2 cannot be factored using real-number coefficients.
Term
 A Strategy for Factoring
Definition
 Always factor out the largest common factor first.Look at the number of termsTwo terms:  Try factoring as a difference of squares first.  Next try factoring as a sum or a difference of cubes.  Do not try to factor as a sum of squares.Three Terms:  Try factoring as the square of a binomial.  Next, try using the grouping method for factoring a trinomial.Four or more terms:  Try factoring by grouping and factoring out a common binomial factor.Always factor completely.  If a factor with more than one term can itself be factored further, do so.
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