the model represents a polynomial of the form ax² + bx + c. which equation is represented by the model? 3x²…

Explanation:

Step1: Count the number of $x^{2}$ - terms

There are 3 positive $x^{2}$ - terms, so the coefficient of $x^{2}$ is 3.

Step2: Count the number of $x$ - terms

There are 2 positive $x$ - terms and 6 negative $x$ - terms. $2x-6x=-4x$, so the coefficient of $x$ is - 4.

Step3: Count the constant - terms

There is 1 positive and 1 negative constant - term, $1 - 1 = 0$ (but we can also expand the factored forms to check). Now expand the factored forms:

• Expand $(3x + 1)(x - 1)$:
  • Using FOIL method: $(3x\times x)+(3x\times(-1))+(1\times x)+(1\times(-1))=3x^{2}-3x + x-1=3x^{2}-2x - 1$.
• Expand $(3x - 1)(x + 1)$:
  • Using FOIL method: $(3x\times x)+(3x\times1)+(-1\times x)+(-1\times1)=3x^{2}+3x - x-1=3x^{2}+2x - 1$.
• Expand $(3x - 1)(x - 1)$:
  • Using FOIL method: $(3x\times x)+(3x\times(-1))+(-1\times x)+(-1\times(-1))=3x^{2}-3x - x + 1=3x^{2}-4x + 1$.
• Expand $(3x - 1)(x - 1)$ (again for clarity):
  • $3x\times x-3x\times1-1\times x + 1\times1=3x^{2}-3x - x+1=3x^{2}-4x + 1$.

Answer:

C. $3x^{2}-4x + 1=(3x - 1)(x - 1)$