SAT Questions that focus on Factoring require knowledge of the following topics.
Factoring (or factorization) consists of writing a mathematical expression as a product of smaller or simpler factors.
The following factoring methods are the ones most often found in SAT questions:
Factoring (or factorization) consists of writing a mathematical expression as a product of smaller or simpler factors.
The following factoring methods are the ones most often found in SAT questions:
Grouping
ax + 2z + 2x + az =
ax +az +2x +2z =
a.(x+z) +2.(x+z) =
(a+2) (x+z)
Grouping - Classic Case 1
x² + ax + bx + ab =
x (x + a) + b (x + a) =
(x + a) (x + b)
Grouping - Classic Case 2
x² - ax - bx + ab =
x (x - a) - b (x - a) =
(x - a) (x - b)
ax + 2z + 2x + az =
ax +az +2x +2z =
a.(x+z) +2.(x+z) =
(a+2) (x+z)
Grouping - Classic Case 1
x² + ax + bx + ab =
x (x + a) + b (x + a) =
(x + a) (x + b)
Grouping - Classic Case 2
x² - ax - bx + ab =
x (x - a) - b (x - a) =
(x - a) (x - b)
Binomial expansions
a² + 2ab + b² = (a + b)²
a² - 2ab + b² = (a - b)²
a³ + 3a²b + 3ab² + b³ = (a + b)³
a³ - 3a²b + 3ab² - b³ = (a - b)³
a² + 2ab + b² = (a + b)²
a² - 2ab + b² = (a - b)²
a³ + 3a²b + 3ab² + b³ = (a + b)³
a³ - 3a²b + 3ab² - b³ = (a - b)³
Difference of two squares
a² - b² = (a + b)(a - b)
a² - b² = (a + b)(a - b)
Sum and difference of two cubes
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
Solved SAT Practice Tests
Find Practice Tests in the following link:
SAT Practice Tests - Factoring
Additional Practice Tests - Factoring
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