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Chapter 5: Problem 35

Find each product of the monomial and the polynomial. $$4 x(x+3)$$

Short Answer

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

Step by step solution

01

Identification of the Monomial and the Polynomial

Identify the parts of the problem. The monomial in this exercise is \(4x\), and the polynomial is \(x + 3\). It's important to keep track of these as they form the key parts of the problem.
02

Application of the Distributive Property

Multiply the monomial with each term of the polynomial. This means you'll multiply \(4x\) by \(x\), then \(4x\) by \(3\).
03

Solve the Multiplication

Now you can calculate the multiplications. \(4x\) multiplied by \(x\) gives \(4x^2\), and \(4x\) multiplied by \(3\) gives \(12x\).
04

Combine the Results

Combine the results from the multiplication. This gives the final result as \(4x^2 + 12x\).

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Most popular questions from this chapter

Make Sense? In Exercises \(96-99\), determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I divide monomials by dividing coefficients and subtracting exponents.

Perform the indicated computations. Express answers in scientific notation. $$\left(2 \times 10^{2}\right)\left(2.6 \times 10^{-3}\right) \div\left(4 \times 10^{3}\right)$$

Use a vertical format to find each product. $$\begin{array}{r}n^{4}-n^{3}+n^{2}-n+1 \\\2 n+3 \\\\\hline\end{array}$$

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