Question

Factorise the following:

3x² + 13x + 14

Answer 1

Given: 3x² + 13x + 14

Step-wise calculation:

1. Multiply the coefficient of x² term and the constant term:

3 × 14 = 42

2. Find two numbers whose product is 42 and sum is 13 the coefficient of the x term.

These numbers are 7 and 6 because,

7 × 6 = 42 and 7 + 6 = 13

3. Rewrite the middle term using 7 and 6:

3x² + 7x + 6x + 14

4. Group terms:

(3x² + 7x) + (6x + 14)

5. Factor out the common factors in each group:

x(3x + 7) + 2(3x + 7)

6. Factor out the common binomial factor:

(x + 2)(3x + 7)