Skip to main content
Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 81
Chapter 1, Problem 81

Perform each division. See Examples 7 and 8. (15m3+25m2+30m)/(5m3)(15m^3+25m^2+30m)/(5m^3)

Verified step by step guidance
1
Identify the division problem: \(\frac{15m^3 + 25m^2 + 30m}{5m^3}\).
Rewrite the division as separate fractions for each term in the numerator: \(\frac{15m^3}{5m^3} + \frac{25m^2}{5m^3} + \frac{30m}{5m^3}\).
Simplify each fraction by dividing the coefficients and subtracting the exponents of like bases: For example, \(\frac{15}{5} = 3\) and \(m^{3-3} = m^0 = 1\) for the first term.
Apply the same process to the other terms: \(\frac{25}{5} = 5\) and \(m^{2-3} = m^{-1}\); \(\frac{30}{5} = 6\) and \(m^{1-3} = m^{-2}\).
Write the simplified expression by combining the simplified terms: \(3 + 5m^{-1} + 6m^{-2}\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4m
Was this helpful?

Key Concepts

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

Polynomial Division

Polynomial division involves dividing each term of the numerator polynomial by the denominator, especially when the denominator is a monomial. This process simplifies the expression by reducing powers and coefficients accordingly.
Recommended video:
Guided course
05:13
Introduction to Polynomials

Properties of Exponents

When dividing terms with the same base, subtract the exponents of the denominator from those of the numerator. For example, m^3 ÷ m^3 equals m^(3-3) = m^0 = 1, which helps simplify each term in the division.
Recommended video:
Guided course
04:06
Rational Exponents

Simplifying Rational Expressions

Simplifying rational expressions means reducing fractions by canceling common factors in numerator and denominator. After dividing each term, combine the simplified terms to write the expression in its simplest form.
Recommended video:
Guided course
05:07
Simplifying Algebraic Expressions
Related Practice
Textbook Question

For the decimal number 46.249, round to the place value indicated. (a) hundredths (b) tenths (c) ones or units (d) tens

Textbook Question

For the decimal number 46.249, round to the place value indicated. (a) hundredths (b) tenths (c) ones or units (d) tens

1
views
Textbook Question

Match each expression in Column I with its equivalent expression in Column II.

2
views
Textbook Question

Factor each polynomial. See Examples 5 and 6. 27-(m+2n)3

Textbook Question

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. M ∩ R

Textbook Question

Simplify each radical. Assume all variables represent positive real numbers. ∛(16 (-2)⁴ (2)⁸)

2
views