Question

Factorise the following:

3x² + 7x + 2

Answer 1

Given expression: 3x² + 7x + 2

Step-wise calculation:

1. Identify a = 3, b = 7 and c = 2.

2. Calculate the product of a and c: 3 × 2 = 6.

3. Find two numbers that multiply to 6 and add to 7 these are 6 and 1.

4. Split the middle term 7x into 6x + 1x:

3x² + 6x + 1x + 2

5. Group terms:

(3x² + 6x) + (1x + 2)

6. Factor each group:

3x(x + 2) + 1(x + 2)

7. Factor out the common binomial:

(3x + 1)(x + 2)