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Chapter 5: Problem 94

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

Short Answer

Expert verified
The result of dividing the polynomial \(3x^2 + 5x - 2\) by the monomial \(x\) is \(3x + 5 - 2/x\).

Step by step solution

01

Identify the Polynomial and the Monomial

To begin with, clearly identify the polynomial and the monomial. We can consider dividing the polynomial \(3x^2 + 5x - 2\) by the monomial \(x\). In this case, \(3x^2 + 5x - 2\) is the polynomial and \(x\) is the monomial.
02

Divide each term of the Polynomial by the Monomial

Next, we proceed to divide each term of the polynomial by the monomial. We do this by dividing the coefficients (numerical parts) and subtracting the exponents if the terms have common variables. Hence, \(3x^2\) divided by \(x\) will be \(3x\), \(5x\) divided by \(x\) will be \(5\), and \(-2\) divided by \(x\) will be \(-2/x\) or \(-2x^{-1}\).
03

Write out the Result

The final step is to express the result of the division. Combining the outputs from the previous step, the result of dividing the polynomial \(3x^2 + 5x - 2\) by the monomial \(x\) will be \(3x + 5 - 2x^{-1}\) or \(3x + 5 - 2/x\).

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Most popular questions from this chapter

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

In each exercise, find the product. $$4 x^{3}\left(4 x^{2}-3 x+1\right)$$

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

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

In Exercises \(79-82,\) simplify each expression. $$\frac{2 x^{3}(4 x+2)-3 x^{2}(2 x-4)}{2 x^{2}}$$
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