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Is the following statement true or false: Polynomials and radical expressions differ because...

Question:

Is the following statement true or false?

Polynomials and radical expressions differ because radical expressions contain rational numbers as exponents and polynomials do not.

Polynomials and Radicals

Polynomial Function is a function involving only non-negative integers powers.

Examples of polynomial functions are quadratic, cubic, and many more. These polynomials are named through its degree.

Illustrations:

$$f(x)=x^{3}+2x^{2}+1 $$

$$f(x)=5x^{8}+x^{3}+7x+15 $$

Radical Function is a function that contains a square root, cube root, ... nth root.

Illustrations:

$$f(x)=\sqrt{x^{3}+x+3} $$

$$f(x)=\sqrt{3x^{4}+x+2} $$

Answer and Explanation:

The answer is true.

Polynomials and radical expressions differ because radical expressions or functions contain rational numbers as exponents and polynomials only involve a non-negative integers powers. Radical functions can have a negative exponent that means taking the reciprocal and making the exponent positive.

Example:

$$f(x)=\sqrt[2]{x^{-5}}=x^{\frac{-5}{2}}=\frac{1}{x^{\frac{5}{2}}}=\frac{1}{\sqrt[2]{x^{5}}} $$


Learn more about this topic:

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What is a Radical Function? - Definition, Equations & Graphs

from Math 105: Precalculus Algebra

Chapter 9 / Lesson 6
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