Question

the model represents the factorization of $2x^2 + 5x + 3$. what are the factors of the polynomial? options: $(2x + 3)(x + 1)$, $(2x - 3)(x - 1)$, $(3x + 2)(x + 1)$, $(3x - 2)(x - 1)$

Explanation:

Step1: Expand each option

• Option 1: \((2x + 3)(x + 1)=2x^2+2x + 3x+3=2x^2 + 5x+3\)
• Option 2: \((2x - 3)(x - 1)=2x^2-2x-3x + 3=2x^2-5x + 3\)
• Option 3: \((3x + 2)(x + 1)=3x^2+3x+2x + 2=3x^2+5x + 2\)
• Option 4: \((3x - 2)(x - 1)=3x^2-3x-2x + 2=3x^2-5x + 2\)

Step2: Compare with the polynomial

The given polynomial is \(2x^2+5x + 3\), which matches the expansion of \((2x + 3)(x + 1)\).

Answer:

A. \((2x + 3)(x + 1)\)