Which statement is true about the equation (x - 4)(x + 2) = 16?
The equation x - 4 = 16 can be used to solve for a solution of the given equation.
The standard form of the equation is x²- 2x - 8 = 0.
The factored form of the equation is (x + 4)(x - 6) = 0.
One solution of the equation is x = -6.

Solution:

Given, the equation is (x - 4)(x + 2) = 16.

We have to find the statement that is true about the given equation.

Considering (x - 4)(x + 2),

(x - 4)(x + 2) = x(x) + x(2) - 4(x) - 4(2)

= x² + 2x - 4x - 8

= x² - 2x - 8

Now, x² - 2x - 8 = 16

x² - 2x - 8 - 16 = 0

x² - 2x - 24 = 0

On factorising x² - 2x - 24,

By splitting the middle term,

x² - 2x - 24 = x² + 6x - 4x - 24

= x(x + 6) - 4(x + 6)

= (x - 4)(x + 6)

Now, (x - 4)(x + 6) = 0

x - 4 = 0

So, x = 4

Similarly, x + 6 = 0

x = -6

Therefore, the factored form of the given equation is (x - 4)(x + 6).

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Which statement is true about the equation (x - 4)(x + 2) = 16?

Summary:

One solution of the equation is x = -6 is true about the equation (x - 4)(x + 2) = 16.