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Simplifying Rational Expressions: (3x^3+5x^2-16x+2)/(x+4)
Introduction
Rational expressions are a fundamental concept in algebra, and simplifying them is an essential skill for any student or math enthusiast. In this article, we will explore how to simplify the rational expression (3x^3+5x^2-16x+2)/(x+4).
Factoring the Numerator
To simplify the expression, we need to factor the numerator, which is a cubic expression. Let's start by factoring out the greatest common factor (GCF) of the numerator, which is x + 2.
(3x^3+5x^2-16x+2) = (x + 2)(3x^2 - 7x + 1)
Simplifying the Expression
Now that we have factored the numerator, we can rewrite the expression as:
(x + 2)(3x^2 - 7x + 1) / (x + 4)
Cancellation
Since x + 2 is a common factor of both the numerator and the denominator, we can cancel it out.
(3x^2 - 7x + 1) / (x + 4)
And that's the simplified form of the rational expression (3x^3+5x^2-16x+2)/(x+4)!
Conclusion
In this article, we have learned how to simplify the rational expression (3x^3+5x^2-16x+2)/(x+4) by factoring the numerator and canceling out common factors. This process is a crucial step in many algebraic manipulations and is essential for solving equations and inequalities.
