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Chapter 2: Problem 20

Use long division to divide. \((8 x-5) \div(2 x+1)\)

Short Answer

Expert verified
The result of the polynomial division is \(4 - \frac{9}{2x+1}\).

Step by step solution

01

Set up the long division

Firstly, set up the division. Write the divisor \(2x + 1\) and dividend \(8x - 5\) into the division symbol.
02

Divide the first terms

Divide the first term of the divisor (2x) into the first term of the dividend (8x). It gives us \(4\). We place this above the division symbol at the place of the initial term.
03

Multiply and subtract

Now, multiply \(4\) by the divisor \(2x + 1\). Subtract the result \(8x+4\) from the dividend \(8x - 5\). This gives us \(-9\).
04

Repeat if necessary

We cannot continue the division since the degree of the new remainder (-9) is less than the degree of the divisor \(2x + 1\). Thus, \(-9\) is our remainder.
05

Write the final answer

The final answer is the term we got above the division symbol and the remainder. The remainder is written as a fraction with the divisor as the denominator. Hence, \(4 - \frac{9}{2x+1}\) is the final answer.

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Most popular questions from this chapter

Determine whether each value of \(x\) is a solution of the inequality. Inequality. \(x^{2}-3<0 \quad\) (a) \(x=3 \quad\) (b) \(x=0\) (c) \(x=\frac{3}{2}\) (d) \(x=-5\)

Solve the inequality and graph the solution on the real number line. \(\frac{3}{x-1}+\frac{2 x}{x+1}>-1\)

(a) find the interval(s) for \(b\) such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients. \(2 x^{2}+b x+5=0\)

Solve the inequality and write the solution set in interval notation. \(2 x^{3}-x^{4} \leq 0\)

Solve the inequality. (Round your answers to two decimal places.) \(\frac{2}{3.1 x-3.7}>5.8\)
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