Textbook Question
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 2 and 17
1627
views
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 66
Factor completely, or state that the polynomial is prime.
Verified step by step guidance1
Identify the greatest common factor (GCF) of the terms in the polynomial \$5x^3 - 45x$. The GCF is the largest expression that divides both terms evenly.
Factor out the GCF from each term. Since the GCF is \$5x$, rewrite the polynomial as \(5x(\ldots)\).
Divide each term by the GCF to find the remaining factor inside the parentheses: \(5x^3 \div 5x = x^2\) and \(-45x \div 5x = -9\).
Write the factored form as \$5x(x^2 - 9)$.
Recognize that \(x^2 - 9\) is a difference of squares, which can be factored further using the formula \(a^2 - b^2 = (a - b)(a + b)\). Here, \(a = x\) and \(b = 3\), so factor it as \((x - 3)(x + 3)\).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring Polynomials
Factoring polynomials involves rewriting a polynomial as a product of simpler polynomials or factors. This process helps simplify expressions and solve polynomial equations. Common methods include factoring out the greatest common factor, grouping, and special products.
Recommended video:
Guided course
07:30
Introduction to Factoring Polynomials
Greatest Common Factor (GCF)
The greatest common factor is the largest expression that divides all terms of a polynomial without leaving a remainder. Factoring out the GCF is often the first step in factoring polynomials, simplifying the expression and making further factoring easier.
Recommended video:
5:57Graphs of Common Functions
Prime Polynomials
A prime polynomial is one that cannot be factored further over the set of real numbers. After attempting all factoring methods, if no factors other than 1 and the polynomial itself are found, the polynomial is considered prime.
Recommended video:
Guided course
07:30Introduction to Factoring Polynomials
Related Practice
Textbook Question
In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (3x4 y2+5x3 y−3y)−(2x4 y2−3x3 y−4y+6x)
1021
views
Textbook Question
Evaluate each expression 1251/3.
1308
views
Textbook Question
In Exercises 33–68, add or subtract as indicated. (4x2+x−6)/(x2+3x+2)−3x/(x+1)+5/(x+2)
1121
views
Textbook Question
Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number.
989
views
Textbook Question
Write each number in decimal notation without the use of exponents.
1037
views