Which equations can be used to find a root of 3x^2+7x+2=0 when factoring and using the zero product property? A) x+1=0 B) x+2=0 C) 3x+2=0 D) 3x+7=0 E) 3x+1=0

## Step 1: Factoring the quadratic equation<br />### To solve the quadratic equation $3x^2 + 7x + 2 = 0$ using the zero product property, we first need to factor it. We look for two numbers that multiply to $(3)(2) = 6$ and add up to $7$. These numbers are $6$ and $1$. We rewrite the middle term as the sum of these two numbers multiplied by $x$: $3x^2 + 6x + x + 2 = 0$. Now, we factor by grouping: $3x(x+2) + 1(x+2) = 0$. This gives us $(3x+1)(x+2) = 0$.<br /><br />## Step 2: Applying the zero product property<br />### The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero: $3x+1=0$ or $x+2=0$.