Question

factor completely.
4u² - 6u - 4

Explanation:

Step1: Find GCF of coefficients

The coefficients are 4, -6, -4. GCF of 4, 6, 4 is 2. So factor out 2:
$2(2u^2 - 3u - 2)$

Step2: Factor quadratic trinomial

Factor $2u^2 - 3u - 2$. Find two numbers: $a \times c = 2 \times (-2) = -4$, and $a + b = -3$. The numbers are -4 and 1.
Rewrite middle term: $2u^2 - 4u + u - 2$
Group: $(2u^2 - 4u) + (u - 2) = 2u(u - 2) + 1(u - 2) = (2u + 1)(u - 2)$

Step3: Combine with GCF

$2(2u + 1)(u - 2)$

Answer:

$2(2u + 1)(u - 2)$