Part A:

Question

How can you factor this trinomial so that you can use the zero product property?

x2+8x+12=0

(1 point)
Responses

(x−2)(x+6)=0
open paren x minus 2 close paren times open paren x plus 6 close paren is equal to 0

(x−2)(x−6)=0
open paren x minus 2 close paren times open paren x minus 6 close paren is equal to 0

(x+2)(x+6)=0
open paren x plus 2 close paren times open paren x plus 6 close paren is equal to 0

(x+2)(x−6)=0
open paren x plus 2 close paren times open paren x minus 6 close paren is equal to 0
Question 2
Part B:

What would the solutions be?

(1 point)
Responses

x=−2 and x=−6
x=−2 and x=−6

x=2 and x=6
x=2 and x=6

x=2 and x=−6
x=2 and x=−6

x=−2 and x=6

Answer 1

To factor the trinomial \(x^2 + 8x + 12 = 0\), we need to find two numbers that multiply to \(12\) (the constant term) and add to \(8\) (the coefficient of \(x\)). The numbers \(2\) and \(6\) meet these criteria, so we can factor the trinomial as follows:

\[ (x + 2)(x + 6) = 0 \]

Thus, the correct response for Part A is: \[ (x+2)(x+6)=0 \]

Part B

Next, to find the solutions, we can use the zero product property. We set each factor to zero:

1. \(x + 2 = 0 \Rightarrow x = -2\)
2. \(x + 6 = 0 \Rightarrow x = -6\)

Therefore, the solutions are: \[ x = -2 \quad \text{and} \quad x = -6 \]

So, the correct response for Part B is: \[ x=−2 \text{ and } x=−6 \]