What is the degree of the polynomial [tex]x^2+6 x+7[/tex]?
Answer (2)
The degree of a polynomial is the highest power of the variable.
Identify the terms in the polynomial: x 2 , 6 x , and 7 .
Determine the powers of x in each term: 2, 1, and 0.
The highest power is 2, so the degree of the polynomial is 2 .
Explanation
Understanding the Problem We are asked to find the degree of the polynomial x 2 + 6 x + 7 . The degree of a polynomial is the highest power of the variable in the polynomial.
Identifying the Powers In the polynomial x 2 + 6 x + 7 , we have three terms: x 2 , 6 x , and 7 . The powers of x in these terms are 2, 1, and 0, respectively (since 7 = 7 x 0 ).
Determining the Degree The highest power of x in the polynomial is 2. Therefore, the degree of the polynomial is 2.
Final Answer The degree of the polynomial x 2 + 6 x + 7 is 2.
Examples
Understanding the degree of a polynomial is crucial in many areas of mathematics and physics. For example, when analyzing the motion of a projectile, the height of the projectile as a function of time can often be modeled by a quadratic polynomial (degree 2). The degree helps determine the general shape and behavior of the function, such as whether it has a maximum or minimum value. In engineering, polynomial functions are used to approximate complex relationships, and the degree of the polynomial affects the accuracy and complexity of the model.
The degree of the polynomial x 2 + 6 x + 7 is 2, which is determined by identifying the highest power of the variable present in the polynomial's terms. The terms are x 2 , 6 x , and 7 , with powers of 2, 1, and 0 respectively. Since 2 is the highest power, the degree is 2.
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