Question

factor completely. $48h^2 - 88h + 24$

Explanation:

Step1: Find the GCF of coefficients

The coefficients are 48, -88, and 24. The GCF of 48, 88, and 24 is 8.
$$48h^2 - 88h + 24 = 8(6h^2 - 11h + 3)$$

Step2: Factor the quadratic

We need two numbers that multiply to \(6\times3 = 18\) and add to -11. The numbers are -9 and -2.
Rewrite the middle term:
$$6h^2 - 9h - 2h + 3$$
Group and factor:
$$(6h^2 - 9h) + (-2h + 3) = 3h(2h - 3) - 1(2h - 3) = (3h - 1)(2h - 3)$$

Step3: Combine results

Putting it all together, the completely factored form is:
$$8(3h - 1)(2h - 3)$$

Answer:

\(8(3h - 1)(2h - 3)\)