Classify the following as linear, quadratic and cubic polynomials:
i) x² + x    ii) x - x³    iii) y + y² + 4    iv) 1 + x    v) 3t
vi) r²    vii) 7x³

Solution:

Let's understand the meaning of a linear, quadratic and cubic polynomial.

A polynomial of degree one is called a linear polynomial represented as ax + b.

A polynomial of degree two is called a quadratic polynomial represented as ax² + bx + c.

A polynomial of degree three is called a cubic polynomial represented as ax³ + bx² + cx + d.

i) x² + x → Quadratic polynomial since the degree is 2.

ii) x - x³ → Cubic polynomial since the degree is 3.

iii) y + y² + 4 → Quadratic polynomial since the degree is 2.

iv) 1 + x → Linear polynomial since the degree is 1.

v) 3t → Liner polynomial since the degree is 1.

vi) r² → Quadratic polynomial since the degree is 2.

vii) 7x³ → Cubic polynomial since the degree is 3.

☛ Check: Class 9 NCERT Solutions Maths Chapter 2 Polynomials

Video Solution:

Classify the following as linear, quadratic and cubic polynomials: (i) x² + x (ii) x - x³ (iii) y + y² + 4 (iv) 1 + x (v) 3t (vi) r² (vii) 7x³

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.1 Question 5:

Summary:

Thus, we see that, 1 + x, 3t are linear polynomials, x² + x, y + y² + 4, r² are quadratic polynomials, and x - x³, 7x³ are cubic polynomials.

☛ Related Questions:

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