Solve for x: x² - 16 = 0.

Solve for x: x² - 16 = 0.

• A. x = 2, -2
• B. x = 4, -4
• C. x = 4, 2
• D. x = 0, 16

Answer: (B)

To solve the equation \( x^2 - 16 = 0 \), the first step is to recognize that this is a difference of squares. The expression can be factored using the formula \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a \) is \( x \) and \( b \) is \( 4 \), since \( 16 \) is \( 4^2 \). Factoring the equation yields: \[ (x - 4)(x + 4) = 0 \] This product will equal zero if either factor is zero. Therefore, we set each factor equal to zero: 1. \( x - 4 = 0 \) leads to \( x = 4 \) 2. \( x + 4 = 0 \) leads to \( x = -4 \) Thus, the solutions to the equation \( x^2 - 16 = 0 \) are \( x = 4 \) and \( x = -4 \). This confirms that the correct answer reflects the values of \( x \) derived from solving the equation, which are both \( 4 \) and \( -4 \

To solve the equation ( x^2 - 16 = 0 ), the first step is to recognize that this is a difference of squares. The expression can be factored using the formula ( a^2 - b^2 = (a - b)(a + b) ). Here, ( a ) is ( x ) and ( b ) is ( 4 ), since ( 16 ) is ( 4^2 ).

Factoring the equation yields:

[

(x - 4)(x + 4) = 0

]

This product will equal zero if either factor is zero. Therefore, we set each factor equal to zero:

1. ( x - 4 = 0 ) leads to ( x = 4 )

2. ( x + 4 = 0 ) leads to ( x = -4 )

Thus, the solutions to the equation ( x^2 - 16 = 0 ) are ( x = 4 ) and ( x = -4 ). This confirms that the correct answer reflects the values of ( x ) derived from solving the equation, which are both ( 4 ) and ( -4 \