Factorising 2x² - 9x + 4

To factorise an expression means to write it as a product of simpler expressions. In order to factorise 2x² - 9x + 4, we need to find two numbers that multiply to 2 x 4 = 8, and add up to -9.

Step 1: Find the factors of 8
The factors of 8 are: 1 x 8 and 2 x 4

Step 2: Determine which factors add up to -9
The only pair of factors that add up to -9 is -1 and -8.

Step 3: Rewrite the expression using the two factors
We can rewrite 2x² - 9x + 4 as 2x² - x - 8x + 4.

Step 4: Group the terms
We can group the first two terms and the last two terms, and factorise each group separately.

2x² - x - 8x + 4 can be written as (2x² - x) - (8x - 4)

Step 5: Factorise each group separately
We can now factorise each group separately.

(2x² - x) - (8x - 4) can be written as x(2x - 1) - 4(2x - 1)

Step 6: Write the final factorised expression
We can see that both terms have a common factor of (2x - 1), so we can write the final factorised expression as:

(2x - 1)(x - 4)

Therefore, the factorised form of 2x² - 9x + 4 is (2x - 1)(x - 4).