Final answer:
The quadratic expression 6x^2 + 11x + 4 can be factorised by finding two numbers that sum to 11 and multiply to 24, which are 8 and 3. Using these numbers to rewrite and group the terms, we can factor by grouping to end up with the factors (2x + 1)(3x + 4).
Step-by-step explanation:
To factorise the quadratic expression 6x^2 + 11x + 4, we are looking for two binomials that multiply together to give us the original expression. The process involves finding two numbers that both add up to the coefficient of the middle term, which is 11, and multiply to give the product of 6 and 4 (the coefficient of the x^2 term and the constant term), which is 24.
These two numbers are 8 and 3, since 8 + 3 = 11 and 8 * 3 = 24. Now we rewrite the middle term, 11x, using 8 and 3:
6x^2 + 8x + 3x + 4
Next, we group the terms to factor by grouping:
- (6x^2 + 8x) + (3x + 4)
- 2x(3x + 4) + 1(3x + 4)
Lastly, we factor out the common binomial factor:
(2x + 1)(3x + 4)