Question

after factoring by grouping, an expression becomes 2x(x + 2) - 3(x + 2). what are the two binomial factors of this expression? (2x-3)(x+2) (2x+3)(x-2) (2x+2)(x-3) (2x-2)(x+3)

Explanation:

Step1: Identify common factor

The expression is \(2x(x + 2)-3(x + 2)\). Both terms have a common binomial factor of \((x + 2)\).

Step2: Factor out common factor

Using the distributive property \(ab+ac=a(b + c)\) (in reverse, factoring out the common factor), we factor out \((x + 2)\) from both terms. So we get \((2x-3)(x + 2)\) since \(2x(x + 2)-3(x + 2)=(2x - 3)(x + 2)\) when we factor out \((x + 2)\).

Answer:

A. \((2x - 3)(x + 2)\)