Question

the model represents the factorization of 2x²+5x+3. what are the factors of the polynomial? (2x+3)(x+1) (2x-3)(x-1) (3x+2)(x+1) (3x-2)(x-1)

Explanation:

Step1: Expand each option

• For \((2x + 3)(x + 1)\):

Using the distributive property (\(a(b + c)=ab+ac\)):
\(2x(x + 1)+3(x + 1)=2x^2+2x+3x + 3=2x^2+5x + 3\).

• For \((2x - 3)(x - 1)\):

\(2x(x - 1)-3(x - 1)=2x^2-2x-3x + 3=2x^2-5x + 3\).

• For \((3x + 2)(x + 1)\):

\(3x(x + 1)+2(x + 1)=3x^2+3x+2x + 2=3x^2+5x + 2\).

• For \((3x - 2)(x - 1)\):

\(3x(x - 1)-2(x - 1)=3x^2-3x-2x + 2=3x^2-5x + 2\).

Step2: Match with the polynomial

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

Answer:

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