Question

which is the factored form of $2x(4x + 3) - (4x + 3)$?
a. $2x - 1$
b. $x(4x + 3)$
c. $2x(4x + 3)$
d. $(2x - 1)(4x + 3)$
e. $(2x + 1)(4x + 3)$

Explanation:

Step1: Identify the common factor

The expression is \(2x(4x + 3)-(4x + 3)\). Notice that \((4x + 3)\) is a common factor in both terms.

Step2: Factor out the common factor

Using the distributive property \(ab - ac=a(b - c)\), here \(a=(4x + 3)\), \(b = 2x\) and \(c = 1\) (since \(-(4x + 3)=-1\times(4x + 3)\)). So we factor out \((4x + 3)\) to get \((4x + 3)(2x-1)\) or \((2x - 1)(4x + 3)\) (since multiplication is commutative).

Answer:

D. \((2x - 1)(4x + 3)\)