Answer :
we have
[tex](x-4)(x+2)=16[/tex]
Step 1
Find the standard form of the equation
[tex](x-4)(x+2)=16[/tex]
[tex]x^{2}+2x-4x-8=16[/tex]
[tex]x^{2}-2x-8-16=0[/tex]
[tex]x^{2}-2x-24=0[/tex]
Step 2
Find the factored form
we have
[tex]x^{2}-2x-24=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-2x=24[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2}-2x+1=24+1[/tex]
[tex]x^{2}-2x+1=25[/tex]
Rewrite as perfect squares
[tex](x-1)^{2}=25[/tex]
Square root both sides
[tex](x-1)=(+/-)5[/tex]
[tex]x=1(+/-)5[/tex]
[tex]x=1+5=6[/tex]
[tex]x=1-5=-4[/tex]
therefore
the equation in factored form is equal to
[tex](x-6)(x+4)=0[/tex]
Step 3
Verify the statements
case A) The equation [tex]x-4=16[/tex] can be used to solve for a solution of the given equation
The statement is False
Because , If you solve the equation
[tex]x-4=16\\x=16+4 \\x=20[/tex]
The value of [tex]x=20[/tex] is not a solution--------> see the procedure
case B) The standard form of the equation is [tex]x^{2}-2x-8=0[/tex]
The statement is False
Because the standard form is equal to [tex]x^{2}-2x-24=0[/tex]
See the procedure
case C) The factored form of the equation is [tex](x-6)(x+4)=0[/tex]
The statement is True
See the procedure
case D) One solution of the equation is [tex]x=-6[/tex]
The statement is False
Because the solutions of the equation are [tex]x=6[/tex] and [tex]x=-4[/tex]
See the procedure
The factored form of the equation is (x + 4)(x – 6) = 0.
Polynomial
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.
Polynomials are classified based on degree as linear, quadratic, cubic and so on.
From the quadratic equation
(x – 4)(x + 2) = 16
x² + 2x - 4x -8 = 16
x² - 2x - 24 = 0
(x + 4)(x - 6) = 0
Find out more on Polynomial at: https://brainly.com/question/2833285