What is the coefficient of $x$ in the expansion of $(x + 3) (x - 5)$ ?

Class 9PolynomialsPolynomials

Step-by-Step Solution

(x + 3) (x - 5) = x^{2} + (3 + (- 5)) x + (3) (- 5) = x^{2} - 2 x - 15

. The coefficient of

x

is the SUM

3 + (- 5) = - 2

; the product −15 is the constant term.

Answer: D) −2

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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