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*To find the GCF in an equation with variables and coefficients, find the GCF of the numbers first then look for the variable with the smallest exponent.
* In dividing in an equation with variables and coefficients, simply subtract the variables. (8x^3/8x = x^2)
1. Find the common factor in all terms.
2. Divide each term to the given monomial factor.
Ex. 8x^3 - 8x = 8x (x^2 - 1)
kr + kb + pr + pb = k (r + b) + p (r + b) = (r + b) (k - p)
Difference of Two Squares:
a^2 - b^2 = (a + b) (a - b)
1. Find the square of each number before separating. If this is not applicable, find the GCF of all factors.
2. Use the formula to factor.
3. Refer to the list of perfect square numbers.
Ex. 25x^2 - 16 = (5x + 4) (5x - 4)
4x^2 - 49y^2 = (2x - 7y) (2x + 7y)
Difference of Two Cubes:
(a^3 + b^3) = (a + b) (a^2 - ab + b^2)
(a^3 - b^3) = (a - b) (a^2 + ab + b^2)
* Remember SOAP (Same, Opposite, Always Positive) for the equations.
1. Find the cube of each number before separating. If this is not applicable, find the GCF of all factors.
2. Use the formula to factor.
3. Refer to the list of perfect cube numbers.
Ex. m^3 + 125 = (m + 5) (m^2 - 5m + 5^2) = (m + 5) (m^2 - 5m + 25)
27x^3 - 64 = (3x - 4) (9x^2 + 12x + 4^2) = (3x - 4) (3x^2 + 12x + 16)
2y^3 - 128 = 2 (y^3 - 64) = 2 (y - 4) (y^2 + 4y + 4^4 or 16)
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