Call Now: (800) 537-1660
 Home    Why?     Free Solver   Testimonials    FAQs    Product    Contact

June 19th

June 19th

# Factoring

## 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:

## III. Difference of Two Squares

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:

## IV. Sum & Difference of Two Cubes

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.

 Prev Next

Home    Why Algebra Buster?    Guarantee    Testimonials    Ordering    FAQ    About Us
What's new?    Resources    Animated demo    Algebra lessons    Bibliography of     textbooks