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# Classify the following as linear, quadratic and cubic polynomials:

i) x^{2} + x ii) x - x^{3 }iii) y + y^{2} + 4 iv) 1 + x v) 3t

vi) r^{2 }vii) 7x^{3}

**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 ax^{2} + bx + c.

A polynomial of degree three is called a cubic polynomial represented as ax^{3} + bx^{2} + cx + d.

i) x^{2} + x → Quadratic polynomial since the degree is 2.

ii) x - x^{3 }→ Cubic polynomial since the degree is 3.

iii) y + y^{2} + 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) r^{2} → Quadratic polynomial since the degree is 2.

vii) 7x^{3} → 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, x^{2} + x, y + y^{2} + 4, r^{2} are quadratic polynomials, and x - x^{3}, 7x^{3 }are cubic polynomials.

**☛ Related Questions:**

- Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. i) 4x² - 3x + 7 ii) y² + √2 iii) 3√t + t√2 iv) y + (2/y) v) x10 + y3 + t50
- Write the coefficients of x² in each of the following:i) 2 + x² + xii) 2 - x² + x³iii) (π/2)x² + xiv) √2x - 1
- Give one example each of a binomial of degree 35, and of a monomial of degree 100.
- Write the degree of each of the following polynomials:i) 5x3 + 4x2 + 7xii) 4 - y2iii) 5t - √7iv) 3

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