Question

Factorise the following:

11 – 8x – 3x²

Answer 1

Given: 11 – 8x – 3x²

Step-wise calculation:

1. Rewrite the expression for clarity:

–3x² – 8x + 11

2. Factor out the leading coefficient with a negative sign to put it into a standard quadratic form:

–(3x² + 8x – 11)

3. Find two numbers whose product is 3 × (–11) = –33 and whose sum is 8. 

Those numbers are 11 and –3 because 11 × (–3) = –33 and 11 + (–3) = 8.

4. Split the middle term using these numbers:

–(3x² + 11x – 3x – 11)

5. Factor by grouping:

–[(3x² + 11x) – (3x + 11)] = –[x(3x + 11) – 1(3x + 11)]

6. Factor out the common factor (3x + 11):

–(x – 1)(3x + 11)

The factorised form is:

11 – 8x – 3x² = –(x – 1)(3x + 11)

Or equivalently:

11 – 8x – 3x² = –(x – 1)(3x + 11)