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Chapter 3: Problem 8

The polynomial \(x^{2}-x-20\) factors as \((x-5)(x+4) .\) What is the quotient of \(\left(x^{2}-x-20\right) \div(x-5) ?\) What is the remainder?

Short Answer

Expert verified
The quotient is \( x + 4 \), and the remainder is 0.

Step by step solution

01

- Factor the Polynomial

The polynomial given is \(x^2 - x - 20\). It is provided that it factors to \( (x - 5)(x + 4) \).
02

- Identify the Quotient and Remainder

To find the quotient, recognize that dividing \(x^2 - x - 20\) by \(x - 5\) is equivalent to finding what you get when canceling out \(x - 5\) from \( (x - 5)(x + 4) \). Therefore, the quotient is \( (x + 4) \).
03

- Confirm Remainder

Since \(x^2 - x - 20\) divides exactly by \(x - 5\), and we are left with a constant polynomial without any remaining terms, the remainder is 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Factoring Polynomials
Factoring polynomials involves expressing a polynomial as a product of its factors. In our exercise, the polynomial is given as \( x^2 - x - 20 \). The task is to find factors such that their product results in the original polynomial. It is provided that \( x^2 - x - 20 \) factors to \( (x - 5)(x + 4) \).

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Most popular questions from this chapter

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