Part A:

Question

How can you factor this trinomial and set it up to use the zero product property to solve?

x2+11x+30=0

(1 point)
Responses

(x−5)(x+6)=0
open paren x minus 5 close paren times open paren x plus 6 close paren is equal to 0

(x+5)(x−6)=0
open paren x plus 5 close paren times open paren x minus 6 close paren is equal to 0

(x−5)(x−6)=0
open paren x minus 5 close paren times open paren x minus 6 close paren is equal to 0

(x+5)(x+6)=0
open paren x plus 5 close paren times open paren x plus 6 close paren is equal to 0
Question 2
Part B:

What are the solutions?

(1 point)
Responses

x=5 and x=6
x=5 and x=6

x=−5 and x=−6
x=−5 and x=−6

x=5 and x=−6
x=5 and x=−6

x=−5 and x=6

Answer 1

To solve the equation \(x^2 + 11x + 30 = 0\) using factoring, we first need to find two numbers that multiply to \(30\) (the constant term) and add up to \(11\) (the coefficient of the \(x\) term).

The correct factorization is: \[ (x + 5)(x + 6) = 0 \]

This means the answer for Part A would be:

(x + 5)(x + 6) = 0

Next, applying the Zero Product Property, we set each factor equal to zero:

1. \(x + 5 = 0\) → \(x = -5\)
2. \(x + 6 = 0\) → \(x = -6\)

Thus, the solutions are:

x = −5 and x = −6

So for Part B, the correct response is:

x = −5 and x = −6