Question

Which polynomial is in standard form? \(x^4 + 3x^3y – 5xy^3 + y^4 – x^4 x^3y^2 + 7xy^3 – 2y^4x^2 + 8a^3 10ab^2 – 12a^2b^3\):

A. Identify the polynomial in standard form.
B. Discuss the significance of standard form in polynomials.
C. Analyze the coefficients and exponents in each term.
D. Evaluate the mathematical properties of the given polynomials.

Answer 1

The polynomial x^4 + 3x^3y – 5xy^3 + y^4 – x^4 x^3y^2 + 7xy^3 – 2y^4x^2 + 8a^3 10ab^2 – 12a^2b^3 is not in standard form. Option A is correct.

Step-by-step explanation:

The polynomial x^4 + 3x^3y – 5xy^3 + y^4 – x^4 x^3y^2 + 7xy^3 – 2y^4x^2 + 8a^3 10ab^2 – 12a^2b^3 is not in standard form.

To write it in standard form, we need to arrange the terms in descending order of exponents.

The standard form of a polynomial is when all the terms are in decreasing order of their exponents, with no like terms combined.

In the given polynomial, the terms are not arranged in descending order of exponents. Therefore, the polynomial is not in standard form.

Option A is correct.