the model represents the factorization of $2x^{2}+5x + 3$. what are the factors of the polynomial? $(2x +…

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

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

Answer

Explanation:

Step1: Expand each option

  • For ((2x + 3)(x + 1)): $$ \begin{align*} (2x+3)(x + 1)&=2x\times x+2x\times1+3\times x+3\times1\ &=2x^{2}+2x+3x + 3\ &=2x^{2}+5x+3 \end{align*} $$
  • For ((2x - 3)(x - 1)): $$ \begin{align*} (2x-3)(x - 1)&=2x\times x-2x\times1-3\times x+(-3)\times(-1)\ &=2x^{2}-2x-3x + 3\ &=2x^{2}-5x+3 \end{align*} $$
  • For ((3x + 2)(x + 1)): $$ \begin{align*} (3x+2)(x + 1)&=3x\times x+3x\times1+2\times x+2\times1\ &=3x^{2}+3x+2x + 2\ &=3x^{2}+5x+2 \end{align*} $$
  • For ((3x - 2)(x - 1)): $$ \begin{align*} (3x-2)(x - 1)&=3x\times x-3x\times1-2\times x+(-2)\times(-1)\ &=3x^{2}-3x-2x + 2\ &=3x^{2}-5x+2 \end{align*} $$

Answer:

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