Question

factor completely.
$2x(6x - 5) - 4(6x - 5)$

a. $5(12x - 24)$ c. $2(6x - 5)(x - 2)$
b. $(6x - 5)(2x - 4)$ d. $2(x - 4)(6x - 5)$

Explanation:

Step1: Identify common factor

Both terms have \((6x - 5)\) as a common factor, and also 2 is a common factor of \(2x\) and \(4\). So factor out \(2(6x - 5)\).
Given expression: \(2x(6x - 5)-4(6x - 5)\)
Factor out \(2(6x - 5)\): \(2(6x - 5)(x - 2)\) (since \(\frac{2x(6x - 5)}{2(6x - 5)}=x\) and \(\frac{- 4(6x - 5)}{2(6x - 5)}=- 2\)? Wait, no, let's do it again. Wait, \(2x(6x - 5)-4(6x - 5)\), factor out \((6x - 5)\) first: \((6x - 5)(2x - 4)\), then factor out 2 from \(2x - 4\): \((6x - 5)\times2(x - 2)=2(6x - 5)(x - 2)\)

Step2: Match with options

Now we check the options. Option c is \(2(6x - 5)(x - 2)\) which matches our result.

Answer:

c. \(2(6x - 5)(x - 2)\)