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Chapter 5: Problem 40

Find each product of the monomial and the polynomial. $$3 x(x-5)$$

Short Answer

Expert verified
The product of the monomial \(3x\) and the polynomial \(x-5\) is \(3x^2 - 15x\).

Step by step solution

01

Identify the monomial and polynomial

The monomial is \(3x\) and the polynomial is \(x-5\). Both terms are separated by a set of parentheses.
02

Distribute the monomial

Distribute the monomial \(3x\) to both terms inside the polynomial. This means multiplying \(3x\) by \(x\) and then \(3x\) by \(-5\).
03

Multiply the terms

Multiplication of like terms results in: \(3x * x = 3x^2\) and \(3x * -5 = -15x\).
04

Write the product of the monomial and polynomial

Combine the multiplication results to form a single expression, and write it in descending order of power. The final answer is \(3x^2 - 15x\).

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Most popular questions from this chapter

Explain the difference between \((-7)^{0}\) and \(-7^{0}\).

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