which statement is true about the equation (x - 4)(x + 2)=16?\nthe equation x - 4 = 16 can be used to solve…

which statement is true about the equation (x - 4)(x + 2)=16?\nthe equation x - 4 = 16 can be used to solve for a solution of the given equation.\nthe standard form of the equation is x² - 2x - 8 = 0.\nthe factored form of the equation is (x + 4)(x - 6)=0.\none solution of the equation is x = -6.

which statement is true about the equation (x - 4)(x + 2)=16?\nthe equation x - 4 = 16 can be used to solve for a solution of the given equation.\nthe standard form of the equation is x² - 2x - 8 = 0.\nthe factored form of the equation is (x + 4)(x - 6)=0.\none solution of the equation is x = -6.

Answer

Explanation:

Step1: Expand the left - hand side

Expand ((x - 4)(x + 2)) using FOIL method. ((x-4)(x + 2)=x^{2}+2x-4x - 8=x^{2}-2x - 8). The original equation becomes (x^{2}-2x - 8=16).

Step2: Convert to standard form

Subtract 16 from both sides of the equation (x^{2}-2x - 8=16) to get the standard - form (x^{2}-2x-24 = 0).

Step3: Factor the quadratic equation

Factor (x^{2}-2x - 24). We need two numbers that multiply to - 24 and add up to - 2. The numbers are - 6 and 4. So (x^{2}-2x - 24=(x + 4)(x - 6)=0).

Step4: Solve for x

Set each factor equal to zero: (x+4 = 0) gives (x=-4) and (x - 6=0) gives (x = 6).

Answer:

The factored form of the equation is ((x + 4)(x - 6)=0).