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Strategies of Factoring: GCF By: Diego Saith and Carlos Salcedo - Coggle…
Strategies of Factoring:
GCF
By: Diego Saith and Carlos Salcedo
2 Terms
Difference of square
Characteristics:Two terms:each term is a perfect sqaure difference
How to factor: (a²-b²a+b)(a-b)
2 Examples
1)x²-64=(x-8)(x+8)
2)36J²-49m²=(6j-7m)(6j+7m)
Difference of cubs
Characteristics:-Two terms -Both terms are perfect cubes -Sum pr a difference
How to factor: a(3)+b(3)=(a+b)(a(2)-ab+b(2))
a(3)-b(3)=(a-b)(a(2)+ab+b(2)
2 Examples
1)x²+8 = (a+b)(a²-2x+4)
2)8a³-216b³ = 8(a³-27b³) = (a²-3ab+9b²) or the normal way (2a-6b)(4a²+12ab+36b²)
3 Terms
x²+bx+c
a=1
Characteristics:
-Trinomial (written in descending order).
-Coefficient of x² is 1.
-2nd term has the same letter but with half of the exponent.
-The 3rd term is a number in most of the cases.
How to factor:
Look for 2 numbers that multiplied give you "c" and added or substrated is "b"
2 examples:
x² - 7x + 12 =
(x-4)(x-3)
3x² + 21xy - 54y² = 3(x² + 7xy - 18y²)
3(x + 9)(x - 2)
PST
Characteristics:
-3 terms (write in descending order)
-The 3rd term is always positive
-The 1st and 3rd term are perfect squares
-The second term is twice the product both squares roots
How to factor:
-Write both squares roots in a binomial squared
a² + 2ab + b² = (a+b)²
a² - 2ab + b² = (a-b)²
2 examples:
x² + 12x + 36
2(6) (x)
(x+6)²
28m² - 28mp + 7p²
7(4m²-4mp+p²)
(2m-p)²
x²+bx+c
a≠1
Characteristics:
-Trinomial (written in descending order)
-Coefficient of x² is 1.
-2nd term has the same letter but with half of the exponent.
-The 3rd term is a number in most of the cases.
How to factor:
You need to multiply the first term with the second term, then find two integers whose product is the multiplication of the first and second term, and whose sum is the 2nd term.
2 examples:
3x² - 10x - 8
3x²+12x+2x-8
3x(x+4)+2(x+4)
(3x-2)(x+4)
8x² - 4x - 24
8x²+16x-12x-24
8x(x+2)-12(x+2)
(8x-12)(x+2)
4 terms
Common Monomial Factor
Characterisitics:
-All of its terms have something in common (a GCF)
How to factor:
Step 1: find GCF of the coeficient and the variables.
Step 2: find the common variable and put it with the least exponent.
2 Examples
1)15x³-15x²+5x=5x(3x²-3x+1)
2)6x²y-21x³y²+3x²y³ = 3x²y(2-7xy+y²)
Common Polynomial Factor
Characteristics
The first 2 terms have a GCF
The other two terms have a GCF
How to factor:
Factor the first two terms and the last 2 terms. This will give you 2 common parentheses and other 2 coefficients, so then group all the common terms
2 Examples
1) 3x³-6x²-x+2
3x²(x-2)-(x-2)
(x-2)(3x²-1)
2) 224az+56ac-84yz-21yc
56a(4z+c)-21y(4z+c)
(56a-21y)(4z+c)