To factorise the quadratic expression 2x² + 7x + 3, we need to find two numbers that multiply to give the product of the coefficient of x² (which is 2) and the constant term (which is 3). This gives us 2 * 3 = 6. We are looking for two numbers that add up to the coefficient of x (which is 7) and multiply to give 6.
The numbers 6 and 1 fit this requirement since:
- 6 + 1 = 7
- 6 * 1 = 6
Next, we rewrite the middle term 7x using 6x + 1x:
2x² + 6x + 1x + 3
Now we can group the terms:
(2x² + 6x) + (1x + 3)
Factor out the common factors in each group:
- From the first group (2x² + 6x), we can factor out 2x: 2x(x + 3)
- From the second group (1x + 3), we can factor out 1: (x + 3)
Now we have:
2x(x + 3) + 1(x + 3)
Notice that (x + 3) is a common factor:
(x + 3)(2x + 1)
So, the factorised form of 2x² + 7x + 3 is:
(x + 3)(2x + 1)