Problem 4 Is the algebraic expression a po... [FREE SOLUTION]

Chapter 0: Problem 4

Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. $$x^{2}-x^{3}+x^{4}-5$$

Short Answer

Expert verified

Yes, the algebraic expression $x^{2}-x^{3}+x^{4}-5$ is a polynomial. It is already in its simplest form and when rearranged in standard form, it becomes $x^{4}-x^{3}+x^{2}-5$.

Step by step solution

- Identify if the expression is a polynomial

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The given algebraic expression $x^{2}-x^{3}+x^{4}-5$ is composed only of terms with power of $x$ being non-negative integers and there are no variable terms in denominators, radicals or absolute values; hence, it is a polynomial.

- Write the polynomial in standard form

To write the polynomial in standard form, remember that we arrange the terms in descending order of their degrees. The highest degree of the terms in our polynomial is 4 (from $x^4$). Arranging in descending order gives us $x^{4}-x^{3}+x^{2}-5$.

- Simplify the polynomial

As there are no like terms to combine, the simplified polynomial in standard form remains $x^{4}-x^{3}+x^{2}-5$.

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91影视

Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. $$x^{2}-x^{3}+x^{4}-5$$

Short Answer

Step by step solution

- Identify if the expression is a polynomial

- Write the polynomial in standard form

- Simplify the polynomial

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