Skip to main content
Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. R - Algebra ReviewProblem 43
Chapter 1, Problem 43

Find each product. See Example 5. 4x² (3x³ + 2x² - 5x +1)

Verified step by step guidance
1
Identify the expression to be multiplied: \(4x^{2} \times (3x^{3} + 2x^{2} - 5x + 1)\).
Apply the distributive property by multiplying \$4x^{2}$ with each term inside the parentheses separately.
Multiply \$4x^{2}\( by the first term: \)3x^{3}$. This gives \(4x^{2} \times 3x^{3} = 12x^{5}\).
Multiply \$4x^{2}\( by the second term: \)2x^{2}$. This gives \(4x^{2} \times 2x^{2} = 8x^{4}\).
Continue by multiplying \$4x^{2}\( by the third term \)-5x$ and the fourth term \(1\), writing each product before combining all terms.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

Key Concepts

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

Polynomial Multiplication

Polynomial multiplication involves distributing each term of one polynomial to every term of the other. This process requires multiplying coefficients and adding exponents of like bases, then combining like terms to simplify the expression.
Recommended video:
5:35
Introduction to Quadratic Equations

Exponent Rules

When multiplying terms with the same base, add their exponents (e.g., x^a * x^b = x^(a+b)). This rule is essential for correctly handling powers of variables during polynomial multiplication.
Recommended video:
03:05
Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem) Example 1

Combining Like Terms

After multiplying, terms with the same variable raised to the same power must be combined by adding or subtracting their coefficients. This step simplifies the polynomial to its standard form.
Recommended video:
3:18
Adding and Subtracting Complex Numbers
Related Practice
Textbook Question

Add or subtract, as indicated. See Example 4. (6m⁴ - 3m² + m) - (2m³ + 5m² + 4m) + (m² - m)

Textbook Question

Multiply or divide, as indicated. See Example 3. ((m² + 3m + 2) / (m² + 5m + 4)) ÷ ((m² + 5m + 6) / (m² + 10m + 24))

9
views
Textbook Question

Find each root. See Example 3. -∜16

5
views
Textbook Question

Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(0)

Textbook Question

Find each product or quotient where possible. See Example 2. -5⁄2 ( 12⁄15 )

Textbook Question

Find each product or quotient where possible. See Example 2. -3⁄8 ( -24⁄9 )

3
views