Test for Polynomials:
Polynomials are algebraic expressions that consist of variables, coefficients, and exponents. They are an important topic in mathematics, particularly in Class 10. To assess your understanding of polynomials, here is a test that covers the key concepts and operations related to polynomials.

Section 1: Polynomial Basics
1. Define a polynomial.
2. Differentiate between a monomial, binomial, and trinomial.
3. State the degree and the leading coefficient of the polynomial: 3x^2 + 4x - 7.
4. Determine whether the following expressions are polynomials or not:
a) √x
b) 2x + 5/x
c) 5x^4 + 2x^3 - x^2 + 7

Section 2: Polynomial Operations
1. Simplify the following expression: (3x^3 - 2x^2 + x) + (-4x^3 + 5x^2 - 3x).
2. Perform the indicated operations and express the result in standard form:
a) (2x^2 - 3x + 4) + (-x^2 + 6x - 1)
b) (3x^2 - 5x + 2)(2x - 4)
c) (2x^3 + 3x^2 - x + 1)/(x - 2)

Section 3: Factorization
1. Factorize the following expressions:
a) x^2 - 9
b) 4x^2 - 25y^2
c) 2x^3 + 8x^2 - 6x

Section 4: Word Problems
1. The length of a rectangle is 4x + 3, and its width is 2x - 1. Find the expression representing the area of the rectangle.
2. The sum of two numbers is 9, and their product is 14. Write a quadratic equation to represent this situation.

Section 5: Miscellaneous
1. Define the terms "zeros" and "roots" of a polynomial.
2. Determine the zeros and the degree of the polynomial: x^4 - 3x^3 + 2x^2 - 6x.

Remember to carefully read each question and provide your answers in a clear and concise manner. Good luck with your test on polynomials!