Question

find the factors
16xu - 24u
8u (2x - 3)
8u (2xu - 3u)
2xu (8 - 12u)
4u (4x - 6)

Explanation:

Step1: Find GCF of 16 and 24

The GCF of 16 and 24 is 8. Also, the common variable terms are \( u \) and \( j \)? Wait, the expression is \( 16xuj - 24uj \). Wait, let's re - examine. The terms are \( 16xuj \) and \( - 24uj \). The GCF of the coefficients 16 and 24 is 8? Wait, no, 16 and 24: factors of 16 are 1,2,4,8,16; factors of 24 are 1,2,3,4,6,8,12,24. GCF is 8? Wait, no, 16 and 24, GCF is 8? Wait, 16 = 8×2, 24 = 8×3. Also, the common variables: both terms have \( u \) and \( j \). Wait, the first term is \( 16xuj=8uj\times2x \), the second term is \( - 24uj = 8uj\times(- 3) \). Wait, but looking at the options, let's check each option:

Option 1: \( 8u(2x - 3) \) – Wait, the original expression is \( 16xuj-24uj \). Let's factor out \( 8uj \)? Wait, no, maybe a typo. Wait, maybe the expression is \( 16xuj - 24uj \), factor out \( 8uj \): \( 8uj(2x - 3) \)? Wait, no, the first option is \( 8u(2x - 3) \) – maybe the \( j \) is a typo. Alternatively, let's check the fourth option: \( 4u(4x - 6) \). Factor out 4u: \( 4u(4x - 6)=16xu - 24u \), but our expression has \( j \). Wait, maybe the original expression is \( 16xu - 24u \) (maybe a typo in the problem, \( j \) is extra). Let's proceed with \( 16xu - 24u \).

Factor out the GCF of 16 and 24, which is 8? Wait, 16 and 24, GCF is 8? 16 = 8×2, 24 = 8×3. And the common variable is \( u \). So factoring out \( 8u \) from \( 16xu-24u \):

\( 16xu - 24u=8u(2x - 3) \)

Let's check other options:

• Option 2: \( 8u(2xu - 3u) \) = \( 16xu^{2}-24u^{2}\) (not matching)
• Option 3: \( 2xj(8 - 12u) \) = \( 16xj-24xju\) (not matching)
• Option 4: \( 4u(4x - 6) \) = \( 16xu-24u \), but if we factor 4u, \( 4u(4x - 6)=4u\times2(2x - 3)=8u(2x - 3) \), but the first option is more simplified.

Step2: Verify the factoring

Multiply \( 8u(2x - 3) \): \( 8u\times2x-8u\times3 = 16xu - 24u \). If we assume the original expression had a typo and the \( j \) was incorrect, this matches.

Answer:

\( 8u(2x - 3) \) (the first option)