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Chapter 5: Problem 109

Explain how to multiply a monomial and a polynomial that is not a monomial. Give an example.

Short Answer

Expert verified
The product of the monomial 3x and binomial \(4x^2 + 1\) is \(12x^3 + 3x\).

Step by step solution

01

Write Out the Monomial and Polynomial

Firstly, let's write out the given monomial and binomial. In this example, the monomial will be 3x, and our polynomial will be \(4x^2 + 1\).
02

Distribute the Monomial

The process of multiplying a monomial by a polynomail involves distributing the monomial to all terms of the polynomial. This means you'll multiple the monomial by each term of the polynomial. In this case that gives us \( (3x * 4x^2) + (3x * 1) \).
03

Multiply

We proceed to execute the multiplication operation we set up in step above. Remember that when multiplying terms with exponents, you add up the exponents. That leaves us with the result of \(12x^3 + 3x\).

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Most popular questions from this chapter

What polynomial, when divided by \(3 x^{2}\), yields the trinomial \(6 x^{6}-9 x^{4}+12 x^{2}\) as a quotient?

Solve: \(4 x-7>9 x-2 .\) (Section 2.7, Example 7)

Explain how to convert from scientific to decimal notation and give an example.

We have seen that in \(2009,\) the United States government spent more than it had collected in taxes, resulting in a budget deficit of \(\$ 1.35\) trillion. The Washington Monument, overlooking the U.S. Capitol, stands about 555 feet tall. Stacked end to end, how many monuments would it take to reach 1.35 trillion feet? (Note: That's more than twice the distance from Earth to the sun.)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Other than multiplying monomials, the distributive property is used to multiply other kinds of polynomials.
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