Problem 1 - College Algebra

Question

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

Step-by-Step Solution

Answer

Yes, the algebraic expression \(2x + 3x^{2} - 5\) is a polynomial, and its standard form is \(3x^{2} + 2x - 5\).

Step 1: Identify if it's a Polynomial

Check if the algebraic expression \(2x + 3x^{2} - 5\) is a polynomial. It is a polynomial because all variables \(x\) have non-negative integer exponents and the operations involved are only addition, subtraction and multiplication.

Step 2: Write the Polynomial in Standard Form

Rewrite the polynomial in standard form. This requires reordering the terms in decreasing order by degree. As such, the given polynomial \(2x + 3x^{2} - 5\) becomes \(3x^{2} + 2x - 5\) when written in standard form.