Question

Factorise the following:

`x^2 + (11x)/6 - 5/3`

Answer 1

Given: `x^2 + (11x)/6 - 5/3`

Step-wise calculation:

Step 1: Remove fractions by multiplying entire expression by 6

`6(x^2 + (11x)/6 - 5/3)`

Distribute:

6x² + 11x – 10

Now we factorise:

6x² + 11x – 10

Step 2: Split the middle term

We need two numbers whose:

Product = 6 × (–10) = –60

Sum = 11

The numbers are 15 and –4

Because 15 + (–4) = 11, 15 × (–4) = –60

Step 3: Rewrite and factor by grouping

6x² + 15x – 4x – 10

Group:

(6x² + 15x) – (4x + 10)

Factor each group:

3x(2x + 5) – 2(2x + 5)

Now take out the common bracket:

(2x + 5)(3x – 2)

Thus:

6x² + 11x – 10 = (2x + 5)(3x – 2)

Step 4: Put back the factor 6

We had multiplied by 6 earlier, so divide by 6:

`x^2 + (11x)/6 - 5/3 = 1/6(2x + 5)(3x - 2)`