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

Multiplying Polynomials

College Algebra

0. Review of Algebra

Multiplying Polynomials

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1:58 minutes

Problem 9

Textbook Question

In Exercises 9–22, multiply the monomial and the polynomial.4x²(3x+2)

Verified step by step guidance

Identify the monomial and the polynomial: The monomial is \(4x^2\) and the polynomial is \(3x + 2\).

Apply the distributive property: Multiply the monomial \(4x^2\) by each term in the polynomial \(3x + 2\).

First, multiply \(4x^2\) by \(3x\): Use the rule \(a^m \cdot a^n = a^{m+n}\) to combine the exponents of \(x\).

Next, multiply \(4x^2\) by \(2\): Simply multiply the coefficients and keep the \(x^2\) term as it is.

Combine the results from the previous steps to express the final expanded polynomial.

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Key Concepts

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

Monomials

A monomial is a mathematical expression that consists of a single term, which can be a number, a variable, or a product of numbers and variables raised to non-negative integer powers. In the given question, '4x²' is a monomial, representing a coefficient (4) multiplied by a variable (x) raised to the power of 2.

Polynomials

A polynomial is an algebraic expression that consists of one or more terms, where each term is a product of a coefficient and variables raised to non-negative integer powers. The expression '3x + 2' is a polynomial with two terms, known as a binomial, which can be added or subtracted to form more complex expressions.

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. This property allows us to multiply a monomial by each term in a polynomial. In the exercise, applying the distributive property means multiplying '4x²' by both '3x' and '2' to find the resulting expression.