Problem 2 - College Algebra Essentials

Question

Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. $$2 x+3 x^{-1}-5$$

Step-by-Step Solution

Answer

The given algebraic expression \(2x + 3x^{-1} - 5\) is not a polynomial because it contains a term with a negative exponent.

Step 1: Identify each term in the algebraic expression

The terms of the equation are \(2x\), \(3x^{-1}\), and \(-5\). A term in an algebraic expression is a numerical or literal expression with its own coefficient.

Step 2: Analyze each term

The first term \(2x\) is a first degree polynomial, as x is raised to the power of 1. The second term \(3x^{-1}\) is not a term in polynomial form, as the exponent is negative which is not allowed in a polynomial. The third term \(-5\) is a zero degree polynomial as it's a constant with no variable attached.

Step 3: Conclude

The expression contains terms that are not polynomials. Therefore, the whole expression \(2x + 3x^{-1} - 5\) is not a polynomial. Hence we can't write it in standard form.