CAT Degree of polynomials - Practice Questions & MCQ

Definition:

The degree of a polynomial is the highest power of the variable in that polynomial.

For instance, in the polynomial , the degree is 3, because the highest power of x is 3.

Foundation Building Questions:

Question 1: 

Given . What is the degree of P(x)?

Solution: 

The term with the highest power of x is . Hence, the degree of P(x) is 4.

Question 2: 

If Q(x) = x - 2, what is the degree of Q(x)?

Solution: 

The highest power of x in the given polynomial is 1. Therefore, the degree of Q(x) is 1.

Tips and Tricks:

1. Identify the Highest Power: Look for the term with the highest power of x (or any other variable being used) to quickly determine the degree.

2. Coefficient Doesn't Matter: Remember, the coefficient (number in front of x) doesn't affect the degree. So in , the degree is 5, regardless of the 7.

3. For Constant Polynomials: If a polynomial is just a constant (e.g., 7, -4, 5), its degree is considered to be 0.

4. Watch for Hidden Powers: Sometimes, terms might be multiplied together. For instance, in the term , the effective power is 2 + 3 = 5.

Remember, understanding the degree of a polynomial helps in many ways: from solving equations, to sketching graphs, to understanding the behaviour of functions. Always give it a quick glance when you come across a polynomial in any problem.