Factorise 3x² − x − 4 by splitting the middle term.

(3x − 4)(x + 1). Multiply first and last coefficients: 3 × (−4) = −12. Two numbers with product −12 and sum −1 are −4 and +3. 3x² − 4x + 3x − 4 = x(3x − 4) + 1(3x − 4) = (3x − 4)(x + 1).

Factorise $3 x^{2} - x - 4$ by splitting the middle term.

Class 9PolynomialsPolynomials

A $(3 x + 4) (x - 1)$
B $(3 x - 1) (x + 4)$
C $(3 x - 4) (x + 1)$
D $(3 x - 2) (x + 2)$

Step-by-Step Solution

Multiply first and last coefficients:

3 \times (- 4) = - 12

. Two numbers with product −12 and sum −1 are −4 and +3.

3 x^{2} - 4 x + 3 x - 4 = x (3 x - 4) + 1 (3 x - 4) = (3 x - 4) (x + 1)

Answer: C)

(3 x - 4) (x + 1)

Key idea: Naming polynomials by terms and degree

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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Factorise 3x2−x−4 by splitting the middle term.

Step-by-Step Solution

Key idea: Naming polynomials by terms and degree

Master this chapter in 30 minutes a day.

More Class 9 Polynomials practice

Factorise $3 x^{2} - x - 4$ by splitting the middle term.