the model represents a polynomial and its factors. which equation is represented by the model? o $x^{2}-2x…

the model represents a polynomial and its factors. which equation is represented by the model? o $x^{2}-2x - 3=(x - 3)(x + 1)$ o $x^{2}-4x + 3=(x - 3)(x - 1)$ o $x^{2}+2x + 3=(x + 3)(x - 1)$ o $x^{2}+4x - 3=(x + 3)(x + 1)$

the model represents a polynomial and its factors. which equation is represented by the model? o $x^{2}-2x - 3=(x - 3)(x + 1)$ o $x^{2}-4x + 3=(x - 3)(x - 1)$ o $x^{2}+2x + 3=(x + 3)(x - 1)$ o $x^{2}+4x - 3=(x + 3)(x + 1)$

Answer

Explanation:

Step1: Expand right - hand side expressions

For option 1: $(x - 3)(x + 1)=x\times x+x\times1-3\times x - 3\times1=x^{2}+x-3x - 3=x^{2}-2x - 3$. For option 2: $(x - 3)(x - 1)=x\times x-x\times1-3\times x+3\times1=x^{2}-x-3x + 3=x^{2}-4x + 3$. For option 3: $(x + 3)(x - 1)=x\times x-x\times1+3\times x-3\times1=x^{2}-x + 3x-3=x^{2}+2x-3$. For option 4: $(x + 3)(x + 1)=x\times x+x\times1+3\times x+3\times1=x^{2}+x+3x + 3=x^{2}+4x + 3$.

Answer:

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