A cardboard box has length $x + 2$ , height $x - 1$ and depth $x$ (all in cm), as shown. Which polynomial gives its volume?

Class 9PolynomialsPolynomials

Step-by-Step Solution

V = x (x + 2) (x - 1) = x (x^{2} + x - 2) = x^{3} + x^{2} - 2 x

. Adding the sides

(3 x + 1)

gives a length, not a volume.

Answer: C)

x^{3} + x^{2} - 2 x

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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