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Chapter 2: Problem 94

Briefly explain how to check polynomial division, and justify your reasoning. Give an example.

Short Answer

Expert verified
To check polynomial division, multiply the divisor with the quotient. If you get the dividend back, the division was correct. This is justified by the fact that multiplication and division are reciprocal operations. Given polynomial division \(x^2 + 3x + 2\) divided by \(x + 1\) gives \(x + 2\). The check confirms the division was performed correctly.

Step by step solution

01

Understand Polynomial Division

Polynomial division refers to the division of two polynomials where the degree of the divisor is less than or equal to the degree of the dividend. In other words, we distribute the divisor into the dividend to get quotient and/or remainder.
02

Justify the Method to Check Polynomial Division

The method to check polynomial division is justified by the reciprocal relation between multiplication and division. After performing polynomial division, you should be able to multiply the divisor with the quotient obtained to get back the dividend if division was performed correctly.
03

Examples: Polynomial Division Check

Let's assume a dividend \(x^2 + 3x + 2\) is divided by a divisor \(x + 1\) and a quotient \(x + 2\) is obtained. To check the division, we multiply back the divisor \(x + 1\) with obtained quotient \(x + 2\), which results in \(x^2 + 3x + 2\), which is the original dividend. So, the polynomial division was performed correctly.

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