Question

In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2x+3x2−5

Accepted Answer

Step 1: Recall the definition of a polynomial. A polynomial is an algebraic expression consisting of terms that are sums or differences of variables raised to non-negative integer powers, multiplied by coefficients. For example, terms like $$3x^2$$, -5x, and 7 are valid in a polynomial. Step 2: Examine the given expression: 2x + $$3x^2 - 5. $$Identify each term and check if it satisfies the criteria for a polynomial. The terms are 2x (a variable raised to the power of 1), $$3x^2 (a $$variable raised to the power of 2), and -5 (a constant term). All terms meet the criteria for a polynomial. Step 3: Write the polynomial in standard form. Standard form means arranging the terms in descending order of the powers of the variable. In this case, the term with the highest power is $$3x^2$$, followed by 2x, and then the constant term -5. Step 4: Rearrange the terms to write the polynomial in standard form: $$3x^2 + 2x - 5. $$Step 5: Verify that the polynomial is now in standard form by confirming that the terms are ordered by decreasing powers of the variable, and all coefficients and exponents are valid for a polynomial.

In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2x+3x²−5

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Key Concepts

Polynomial Definition

Standard Form of a Polynomial

Degree of a Polynomial