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Chapter 5: Problem 110

Explain how to multiply polynomials when neither is a monomial. Give an example.

Short Answer

Expert verified
Multiplying polynomials when neither is a monomial involves multiplying each term in the first polynomial by every term in the second, and then simplifying by combining like terms, if any. Using polynomials \(P(x) = 3x+2\) and \(Q(x) = 2x-1\), the result is \(6x^2 + x - 2\).

Step by step solution

01

Choose Polynomials

Let's choose two polynomials for the demonstration; \(P(x) = 3x + 2\), and \(Q(x) = 2x - 1\).
02

Polynomials Multiplication

Multiply every term in \(P(x)\) with every term in \(Q(x)\). It yields: \((3x * 2x) + (3x * -1) + (2 * 2x) + (2 * -1) = 6x^2 - 3x + 4x - 2\).
03

Combine Like Terms

Finally, combine any like terms in the resulting expressions. So the final answer is \(6x^2 + x - 2\).

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Most popular questions from this chapter

In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{20 x^{7} y^{4}-15 x^{3} y^{2}-10 x^{2} y}{-5 x^{2} y}$$

In Exercises \(105-106,\) find the missing coefficients and exponents designated by question marks. $$\frac{3 x^{14}-6 x^{12}-7 x^{7}}{2 x^{7}}=-x^{7}+2 x^{5}+3$$

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

Express \(\frac{7}{8}\) as a decimal. (Section \(1.3,\) Example 4 )

Use a vertical format to find each product. $$\begin{array}{r} 9 y^{3}-7 y^{2}+5 y \\ 3 y^{2}+5 y \\ \hline \end{array}$$
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