Question

Factorise the following:

15 – 4х – 4x²

Answer 1

Given expression: 15 – 4х – 4x²

Step-wise calculation:

1. Rewrite in standard form for clarity:

–4x² – 4x + 15

2. Multiply the coefficient of x² term and constant:

a × c = (–4) × 15 = –60

a × c = –60

We need two numbers whose product is –60 and sum is the coefficient of x, which is –4.

These numbers are –10 and +6 because:

–10 × 6 = –60

–10 + 6 = –4

3. Split the middle term using –10 and +6:

–4x² – 10x + 6x + 15

4. Group terms:

(–4x² – 10x) + (6x + 15)

5. Take common factors from each group:

–2x(2x + 5) + 3(2x + 5)

6. Take out the common binomial factor:

(2x + 5)(–2x + 3)

7. Rewrite the second factor with the leading term positive:

(2x + 5)(3 – 2x)

The factorised form of 15 – 4x – 4x² is (2x + 5)(3 – 2x) or equivalently (2x + 5)(–2x + 3).