Question

−2x ²+17−15x+7xy

A) Polynomial of degree 2 in x and y.
B) Quadratic polynomial in x.
C) Linear polynomial in x and y.
D) Cubic polynomial in x and y.

Answer 1

The given expression is best classified as a Quadratic polynomial in x (option B), because the highest degree of x present in any term is 2, represented by the term −2x².

Step-by-step explanation:

The expression −2x ²+17−15x+7xy represents a polynomial which can be classified based on the degrees of its terms with respect to the variables x and y. A polynomial's degree is the highest degree of its terms when each term is considered separately. Looking at the given polynomial:

• The term −2x ² has a degree of 2 in x.
• The term −15x has a degree of 1 in x.
• The term 7xy has a degree of 1 in x and 1 in y, making the term's overall degree 2 when considering both variables.

Therefore, the correct classification of the given polynomial is that it is a Quadratic polynomial in x because the highest power of x is 2, which occurs in the term −2x². It can also be considered a Quatreatic polynomial in terms of x and y due to the 7xy term. The terms involving y do not affect the classification in terms of x alone. Hence, the appropriate answer for this polynomial is option (B) Quadratic polynomial in x.