Question

Find the coefficient of x² in the product (x – 1) (x – 5) (x – 6).

Answer 1

Given: Find the coefficient of x² in the product (x – 1)(x – 5)(x – 6).

Step-wise calculation:

1. First multiply two factors:

(x – 1)(x – 5) = x² – 5x – x + 5

(x – 1)(x – 5) = x² – 6x + 5

2. Now multiply the result by the third factor (x – 6): 

(x² – 6x + 5)(x – 6)

3. Expand this product:

= x² × x – x² × 6 – 6x × x + 6x × 6 + 5 × x – 5 × 6

= x³ – 6x² – 6x² + 36x + 5x – 30

4. Combine like terms:

= x³ – (6x² + 6x²) + (36x + 5x) – 30

= x³ – 12x² + 41x – 30

The coefficient of x² in the expanded product (x – 1)(x – 5)(x – 6) is (–12).