CAT Concept of monomials, binomials, trinomials - Practice Questions & MCQ

Definition:

1. Monomial: A polynomial with just one term. Example: 

2. Binomial: A polynomial with two unlike terms. Example: .

3. Trinomial: A polynomial with three unlike terms. Example: .

Application of Concept 1: Remember, regardless of whether it's a monomial, binomial, or trinomial, the degree of the polynomial is still determined by the term with the highest power of the variable.

Foundation Building Questions:

Question 1: 

Which of the following is a binomial of degree 3?

Solution: 

For a polynomial to be a binomial, it should have two terms. Among the given options, both A and B are binomials. However, only option B, 5x3+ 2, has the highest degree term as 3. Therefore, the correct answer is B.

Question 2: 

The polynomial  is a _________?

A) Monomial

B) Binomial

C) Trinomial

D) None of the above

Solution: 

P(x) has three unlike terms. Hence, it is a trinomial. The correct answer is C.

Tips and Tricks:

1. Quick Identification: Count the number of distinct terms:

    - One term? It's a monomial.

    - Two terms? It's a binomial.

    - Three terms? It's a trinomial.

2. Combined Degrees: In binomials and trinomials, always check for like terms. If like terms exist, combine them, which may change the type of polynomial. For instance,  becomes binomial!

3. Degree Doesn't Determine the Type: A trinomial can have degree 1 (like x + 1 - 2x) or higher. The type (mono, bi, tri) depends on the number of terms, not the degree.

4. Application of Degree: Even when you're identifying the type of polynomial, always be ready to identify its degree, especially if it's part of the question or necessary for further calculations.

Grasping the basics of these types of polynomials will provide a foundation for understanding more complex polynomial expressions and equations, especially as you move on to polynomial operations and factoring.