step 1 Long division, x plus 8 into x squared plus 11x plus 16. Divide the first terms, x squared divid

(x^2+11 x+16)/(x+8)

Name: Problem 44, Chapter 4: Beginning and Intermediate Algebra
Uploaded: 2022-02-10T23:58:56-08:00
Duration: 38 s
Channel: James Kiss
Description: (x^2+11 x+16)/(x+8)

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Key Concepts

Domain Restrictions

When handling rational expressions, it is essential to consider domain restrictions, meaning identifying values of the variable that would make the denominator equal to zero. These values must be excluded since they do not yield valid, defined expressions.

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. Simplifying these expressions usually involves factoring and canceling common factors while ensuring that the original restrictions on the variable (such as non-zero denominators) are maintained.

Polynomial Division

Polynomial division, whether by long division or synthetic division, is a method used to divide polynomials, particularly when the degree of the numerator is greater than or equal to that of the denominator. This technique allows one to express the result as a quotient plus a remainder over the original divisor, which can simplify analysis or further manipulation of the expression.

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