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Strategies for factoring - Coggle Diagram
Strategies for factoring
3 terms :
PST
Its caracteristics are that the first and the third term has to be perfect In this process of factorization we have to take the square root of the first and the final terms and the result has to be elevated to the square
- y2+2y +1 = (y+1)2
- 8y2+4y+4=
(4y+2)2
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2 terms
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Difference of squares
Two terms
Two terms each terms is a perfect square, difference: how to factor: Find the square rrot of both and write them as a product of two binomials with a+ and a-. Note: Sum of square can;t be factored (prime) Note: prime means it can't be factored
Examples:
1) x²-64= (x+8)(x-8)
2) 100x² -9= (10x+3)(10x-3)
4 terms (by grouping)
Common Polynomial Factor
Factor by grouping (Case #1 and Case #2). In expressions with 4 or 6 terms, we factor two parts of the expression, then the GCF of two terms (each binomial) and then factor the common polynomial factor.
Examples: GCF and CPF
1) 3x3 -6x2 -x+2 = 3x2(x-2)-(x-2)= (x-2)(3x2-1)
2) 4x3-15 +20x2 -3x = 4x3 + 20x2 -3x -15 (rearrange) 4x2(x+5) -3(x+5) = (4x2-3) (x+5)
Common Monomial Factor
To factor it we have to separete them in a parenthesis and the common term we divide it for the other terms and separate it with its common.
Its Caractheristics are that one must be divisible for minimum 1 term and it always has 2 termsExamples
- 3m2-6mn+4m-8n
(3m2-6mn)+(4m-8n)
3m(m-2n)+4(m-2n)
=(3m+4)(m-2n)
- 2x2 -3xy-4x+6y
(2x2-3xy)- (4x+6y)
x(2x-3y) -2(-2x+3y)
=(2x-3y)(x-2)
MEMBERS OF TEAM: SANTIAGO ARIAS, PAOLO MONROY y CRISTOPHER HERNANDEZ