To factor the quadratic expression $4x^2 - 11x + 6$, we can follow these steps:

1. Identify the coefficients:

   • $a = 4$ (coefficient of $x^2$)
   • $b = -11$ (coefficient of $x$)
   • $c = 6$ (constant term)

2. Multiply $a$ and $c$:

   • $ac = 4 \times 6 = 24$

3. Find two numbers that multiply to $ac$ and add to $b$:

   • We need two numbers that multiply to 24 and add to -11.
   • These numbers are $-3$ and $-8$ because $-3 \times -8 = 24$ and $-3 + -8 = -11$.

4. Rewrite the middle term using these numbers: $4x^2 - 3x - 8x + 6$

5. Factor by grouping:

   • Group the terms: $(4x^2 - 3x) - (8x - 6)$
   • Factor out the common factors in each group: $x(4x - 3) - 2(4x - 3)$
   • Factor out the common binomial factor: $(4x - 3)(x - 2)$

So, the factored form of the quadratic expression $4x^2 - 11x + 6$ is:

$(4x - 3)(x - 2)$

Would you like further details or have any questions about this solution?

Here are some related questions you might find interesting:

1. How do you solve quadratic equations using the quadratic formula?
2. What are the steps to complete the square for a quadratic expression?
3. Can all quadratic expressions be factored easily?
4. How do you find the roots of a quadratic equation?
5. What is the difference between factoring and solving a quadratic equation?

Tip: When factoring quadratics, always look for a pair of numbers that multiply to $ac$ and add to $b$ to split the middle term.