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Chapter 5: Problem 51

Find each product of the monomial and the polynomial. $$\left(x^{2}+5 x-3\right)(-2 x)$$

Short Answer

Expert verified
The product of the monomial \(-2x\) and the polynomial \(x^2+5x-3\) is \(-2x^3-10x^2+6x\).

Step by step solution

01

Identify the monomial and polynomial

The monomial in this problem is \(-2x\) and the polynomial is \(x^2+5x-3\).
02

Distribute the monomial to the polynomial

To distribute the monomial to the polynomial, each term of the polynomial is multiplied by the monomial. Thus, the expression becomes: \[-2x \cdot x^2+(-2x)\cdot5x +(-2x) \cdot -3.\]
03

Simplify each term

After multiplying each term, we get: \[-2x^3-10x^2+6x.\] This is the final simplified form of the expression.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$5^{2} \cdot 5^{-2}>2^{5} \cdot 2^{-5}$$

Use a vertical format to find each product. $$\begin{array}{r}7 x^{3}-5 x^{2}+6 x \\\3 x^{2}-4 x \\\\\hline\end{array}$$

Perform the indicated computations. Express answers in scientific notation. $$\left(5 \times 10^{3}\right)\left(1.2 \times 10^{-4}\right) \div\left(2.4 \times 10^{2}\right)$$

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.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$534.7=5.347 \times 10^{3}$$
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