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Chapter 3: Problem 19

Use long division to divide. $$\left(x^{3}-9\right) \div\left(x^{2}+1\right)$$

Short Answer

Expert verified
The quotient is \(x\), and the remainder is \(-x^{2}-9\). So, the division \((x^{3}-9) \div (x^{2}+1)\) is written as \(x - \frac{x^{2}+9}{x^{2}+1}\).

Step by step solution

01

Match the highest degree terms

First match the highest degree term of the divisor \(x^{2}+1\) with the highest degree term of the dividend \(x^{3}-9\). Corresponding to \(x^{3}\), we select \(x\). We multiply entire divisor with \(x\) to match the highest degree term. Therefore, \(x\) is the first term of our quotient.
02

Subtract from the dividend

Now multiply the divisor by the term obtained above and subtract the result from the original dividend. i.e., \((x^{3}-9) - x\cdot(x^{2}+1) = -x^{2}-9\). This is our new dividend.
03

Repeat the process

Now we repeat the process. We can't match \(x^{2}\) with the highest degree term of \(-x^{2}-9\), as degree of \(-x^{2}-9\) is lesser. Thus, we stop here.
04

Write remaining dividend as the remainder

We write the remaining dividend as remainder. Here the remainder is \(-x^{2}-9\).

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Most popular questions from this chapter

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