Class 9 - Chapter 2: Introduction to Linear Polynomials

Q1: Find the degrees of the following polynomials:

(i) 2x² − 5x + 3

(ii) y³ + 2y − 1

(iii) −9

(iv) 4z − 3

Ans (i) The highest power of x is 2, so that the degree will be 2.

Ans (ii) The highest power of y is 3, so that the degree will be 3.

Ans (iii) The polynomial is a constant, so the degree will be 0.

Ans (iv) The highest power of z is 1, so that the degree will be 1.

Q2: Write polynomials of degrees 1, 2 and 3.

Ans: A polynomial of degree 1 is called a linear polynomial. For example, 2x + 3.

A polynomial of degree 2 is called a quadratic polynomial. For example, x² + 2x + 1.

A polynomial of degree 3 is called a cubic polynomial. For example, x³ + 2x² + x + 1.

Q3: What are the coefficients of x² and x³ in the polynomial x⁴ − 3x³ + 6x² − 2x + 7?

Ans: The coefficient of x² is 6 and the coefficient of x³ is -3.

Q4: What is the coefficient of z in the polynomial 4z³ + 5z² − 11?

Ans: The coefficient of z is 0, since there is no z term in the polynomial.

Q5: What is the constant term of the polynomial 9x³ + 5x² − 8x − 10?

Ans: The constant term is -10. (A term which does not contain any variable is called a constant term)