Problem 5 - Beginning and Intermediate Algebra

Question

When asked to factor a polynomial, what is the first question you should ask yourself?

Step-by-Step Solution

Answer

Is it a monomial, binomial, trinomial, or a polynomial with more terms?" Identifying the type of polynomial helps you determine which strategy you should use in order to factor the given polynomial efficiently.

Step 1: 1. Identifying the type of polynomial

When asked to factor a polynomial, the first question you should ask yourself is "What type of polynomial am I dealing with? Is it a monomial, binomial, trinomial, or a polynomial with more terms?" This question is important because different types of polynomials will require different factoring techniques. Identifying the type of polynomial helps you determine which strategy you should use in order to factor the given polynomial efficiently.

Step 2: 2. Factoring techniques for different polynomials

Depending on the type of polynomial identified in Step 1, you can choose the appropriate factoring technique(s) to use: (a) Monomial: Look for a common factor among all the terms and factor it out. (b) Binomial: Check for difference of squares or difference or sum of cubes. (c) Trinomial: Look for perfect squares (e.g., \( (ax + b)^2\)) or use factoring by grouping, completing the square, or the quadratic formula. (d) Polynomial with more terms: Use factoring by grouping, synthetic division, or the Rational Root Theorem as needed. Remember that it is always a good idea to look for the greatest common factor (GCF) across all terms before using any other factoring technique.