Problem 5 When asked to factor a polynomia... [FREE SOLUTION]

Chapter 7: Problem 5

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

Short Answer

Expert verified

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 by step solution

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.

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

Short Answer

Step by step solution

1. Identifying the type of polynomial

2. Factoring techniques for different polynomials

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Statistics

Discrete Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.