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Chapter 5: Problem 39

Find each product of the monomial and the polynomial. $$2 x(x-6)$$

Short Answer

Expert verified
The product of the monomial \(2x\) and the polynomial \((x - 6)\) is \(2x^2 - 12x\).

Step by step solution

01

Distribute the Monomial to the Polynomial

Begin by distributing the monomial \(2x\) to each term in the polynomial \((x - 6)\). This is done by multiplying \(2x\) with \(x\) and \(2x\) with \(-6\).
02

Multiply the Monomial with the First Term

Multiplying \(2x\) with \(x\) gives \(2x^2\).
03

Multiply the Monomial with the Second Term

Multiplying \(2x\) with \(-6\) gives \(-12x\).
04

Combine the Results

Combine the results from step 2 and 3 to get the final result of the product of the monomial and the polynomial.

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Most popular questions from this chapter

Explain how to divide a polynomial that is not a monomial by a monomial. Give an example.

The mad Dr. Frankenstein has gathered enough bits and pieces (so to speak) for \(2^{-1}+2^{-2}\) of his creature-to-be. Write a fraction that represents the amount of his creature that must still be obtained.

Perform the indicated computations. Express answers in scientific notation. $$\frac{\left(1.2 \times 10^{6}\right)\left(8.7 \times 10^{-2}\right)}{\left(2.9 \times 10^{6}\right)\left(3 \times 10^{-3}\right)}$$

Use a vertical format to find each product. $$\begin{aligned}&3 y^{3}+2 y^{2}+y+4\\\&y+3\end{aligned}$$

Graph \(3 x-2 y=6\) using intercepts. (Section 3.2 Example 4 )
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