Summarizing Greatest Common Factor and Factor By Grouping

Key Concepts

• Finding the Greatest Common Factor (GCF): To find the GCF of two expressions:
  1. Factor each coefficient into primes. Write all variables with exponents in expanded form.
  2. List all factors—matching common factors in a column. In each column, circle the common factors.
  3. Bring down the common factors that all expressions share.
  4. Multiply the factors.
• Factor the Greatest Common Factor from a Polynomial: To factor a greatest common factor from a polynomial:
  1. Find the GCF of all the terms of the polynomial.
  2. Rewrite each term as a product using the GCF.
  3. Use the ‘reverse’ Distributive Property to factor the expression.
  4. Check by multiplying the factors.
• Factor by Grouping: To factor a polynomial with 4 four or more terms
  1. Group terms with common factors.
  2. Factor out the common factor in each group.
  3. Factor the common factor from the expression.
  4. Check by multiplying the factors.

Glossary

factoring

Factoring is splitting a product into factors; in other words, it is the reverse process of multiplying.

greatest common factor

The greatest common factor is the largest expression that is a factor of two or more expressions is the greatest common factor (GCF).