Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Factoring Polynomials

College Algebra

0. Review of Algebra

Factoring Polynomials

Previous problemNext problem

2:08 minutes

Problem 66

Textbook Question

In Exercises 65–92, factor completely, or state that the polynomial is prime. 5x^3−45x

Verified step by step guidance

Identify the greatest common factor (GCF) in the terms of the polynomial. In this case, the GCF of 5x^3 and -45x is 5x.

Factor out the GCF from the polynomial. This involves dividing each term of the polynomial by 5x.

Write the polynomial as a product of the GCF and the resulting polynomial after factoring out the GCF.

Check if the resulting polynomial can be factored further. In this case, the polynomial inside the parentheses is a difference of squares.

Factor the difference of squares using the formula a^2 - b^2 = (a + b)(a - b) if applicable.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Factoring Polynomials

Factoring polynomials involves breaking down a polynomial expression into simpler components, or factors, that when multiplied together yield the original polynomial. This process often includes identifying common factors, using techniques such as grouping, or applying special formulas like the difference of squares or perfect square trinomials.

Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) is the largest factor that divides two or more numbers or terms without leaving a remainder. In polynomial expressions, finding the GCF is crucial as it simplifies the factoring process by allowing you to factor out the GCF from each term, making the remaining polynomial easier to work with.

Prime Polynomials

A prime polynomial is a polynomial that cannot be factored into simpler polynomials with real coefficients. Recognizing when a polynomial is prime is important in algebra, as it indicates that the polynomial does not have any roots or factors other than itself and one, which can affect the solutions to equations involving that polynomial.