Question

Which statement about the simplified polynomial is true?

A) It is degree 4 because the leading coefficient is 4
B) It is degree 4 because the largest power of all terms is 4
C) It is degree 5 because the largest sum of exponents is 5
D) It is degree 5 because the greatest coefficient is 5

Answer 1

Statement B is true regarding the degree of a polynomial, as it is determined by the largest power of the variable present, not by the leading coefficient or sum of exponents.

Step-by-step explanation:

The degree of a polynomial is defined by the largest power of all terms when the polynomial is in its simplified form. The leading coefficient of a polynomial does not determine its degree; therefore, statement A is incorrect. Moreover, the coefficients of the terms do not affect the degree either, making statement D incorrect. Statement B is the correct choice because in a polynomial, the degree is certainly determined by the largest power of the variable present in the polynomial, regardless of the coefficients. Lastly, statement C is not relevant since the sum of exponents does not determine the degree of the polynomial.

When we mention powers such as raising a number to the fourth power, it implies multiplication of that number by itself four times. For example, 4 raised to the 3rd power is 4 x 4 x 4, which is 4³. Similarly, for a polynomial, the term with the highest exponent on the variable indicates the degree of the polynomial.