I. Common Factoring
A. Definition: “Greatest Common Factor” ( GCF ) or “common factor” is a number or
algebraic ex pression that appears in every term of the expression .
B. Examples:
i.
a. Common Factor = 3
b. Factored Form :
ii.
a. Common Factor = 2abc3
b. Factored Form:
II. Trinomials
A. A trinomial may have a common factor, or may factor into the product of two
binomials , or both.
B. Standard form:
C. To factor: Try to find possible combinations of the factors of “a” and “c”
that will result in “b”.
D. Example:
A. Special Formula : i.
B. The difference of two perfect squares can always be factored at least once .
C. The sum of perfect squares can never be factored. They result in imaginary
roots .
D. Examples:
A. Special Formulas:
B. Hint for factoring:
i. The sign between “x” and “a” in the first factor of the product will be the
same sign as the sign between the two cubes. The sign between “x2” and “ax” in the
second factor will be the opposite sign.
C. Examples:
V. Factoring by Grouping
A. Method: Arrange the four terms in two groups of two terms each. Choose any
two terms that have a common factor as a group.
B. Remove any common factor from each group.
C. Remove the common factor from the two terms that result in step 2.
D. Warning: Not all expressions can be factored by grouping. In fact, some
polynomials cannot be factored by any method .
E. Step-by-Step:
| i. ab-b+ac-c |
1. Two groups of two terms |
| ii. b(a-1)+c(a-1) |
2. Remove common factors |
| iii. (a-1)(b+c) |
3. Remove resulting common factors |
F. Examples:
VI. FACTOR COMPLETELY – Some problems may require more
than one factoring step.
