A rectangular lawn of length $2 x$ m and width $x$ m has a path 1 m wide all round it (yellow). Which polynomial gives the area of the path?

Class 9PolynomialsPolynomials

Step-by-Step Solution

Outer rectangle:

(2 x + 2) (x + 2) = 2 x^{2} + 6 x + 4

. Lawn:

2 x^{2}

. Path

= 2 x^{2} + 6 x + 4 - 2 x^{2} = 6 x + 4

Answer: D)

6 x + 4

By number of terms:
- **Monomial**: 1 term (e.g.

5 x^{3}

)
- **Binomial**: 2 terms (e.g.

x^{2} + 3

)
- **Trinomial**: 3 terms (e.g.

x^{2} + 2 x + 1

)

By degree:
- **Linear** (degree 1):

3 x - 5

- **Quadratic** (degree 2):

x^{2} - 4

- **Cubic** (degree 3):

2 x^{3} + x - 1

- **Biquadratic** (degree 4):

x^{4} + 1

A polynomial can fit multiple categories.

5 x^{3}

is both a monomial and a cubic.

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