Textbook Question
Write an equation in point-slope form and slope-intercept form of the line passing through (-10,3) and (-2,-5).
944
views
Ch. 3 - Polynomial and Rational Functions
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 4, Problem 114
Rewrite 4-5x-x2+6x3 in descending powers of x.
Verified step by step guidance1
Identify the powers of x in each term of the polynomial: 4 (which is x^0), -5x (which is x^1), -x^2, and 6x^3.
Recall that descending powers of x means arranging the terms starting from the highest power of x to the lowest power.
Determine the order of powers from highest to lowest: x^3, x^2, x^1, and x^0.
Rewrite the polynomial by placing the terms in order of descending powers: start with the term containing x^3, then x^2, then x^1, and finally the constant term.
Express the polynomial as .
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Terms and Powers
A polynomial is an expression consisting of variables raised to non-negative integer powers, combined using addition or subtraction. Each term includes a coefficient and a power of the variable, such as x^3 or x^2. Understanding the structure of polynomial terms is essential for rearranging them.
Recommended video:
04:10
Powers of i
Descending Order of Powers
Writing a polynomial in descending order means arranging its terms from the highest power of the variable to the lowest. This standard form helps in comparing, adding, or subtracting polynomials and is crucial for clarity and further operations.
Recommended video:
04:10Powers of i
Combining Like Terms
Like terms have the same variable raised to the same power and can be combined by adding or subtracting their coefficients. Recognizing and combining like terms simplifies the polynomial before ordering it, ensuring the expression is in its simplest form.
Recommended video:
5:22Combinations
Related Practice
Textbook Question
Exercises 107–109 will help you prepare for the material covered in the next section. Determine whether f(x)=x4−2x2+1 is even, odd, or neither. Describe the symmetry, if any, for the graph of f.
851
views
Textbook Question
Use (2x3−3x2−11x+6)/(x−3)=2x2+3x−2 to factor 2x3-3x2-11x+6 completely.
1010
views
Textbook Question
Divide 737 by 21 without using a calculator. Write the answer as quotient + remainder/divisor
513
views