Gwen was asked to solve 3x2−20=7

Question

by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses

x=−3
, x=3
x equals negative 3 , x equals 3

x=−3
x equals negative 3

x=9
, x=−9
x equals 9 , x equals negative 9

x=3

Answer 1

To solve the equation \( 3x^2 - 20 = 7 \) by factoring using the difference of squares pattern, we first rewrite the equation:

1. Move 7 to the left side: \[ 3x^2 - 20 - 7 = 0 \implies 3x^2 - 27 = 0 \]

2. Factor the left side: We can factor this as: \[ 3(x^2 - 9) = 0 \]

3. Recognize that \( x^2 - 9 \) is a difference of squares: \[ 3(x - 3)(x + 3) = 0 \]

4. Set each factor to zero: \[ 3 = 0 \text{ (not applicable)} \] \[ x - 3 = 0 \implies x = 3 \] \[ x + 3 = 0 \implies x = -3 \]

Therefore, the solutions are \( x = -3 \) and \( x = 3 \).

So, the correct responses would be:

• \( x = -3, x = 3 \)
• \( x \text{ equals negative 3, } x \text{ equals } 3 \)

Both of these options represent the same solutions.