Question

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

Answer 1

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

Answer 2

we have

$(x-4)(x+2)=16$

Step 1

Find the standard form of the equation

$(x-4)(x+2)=16$

$x^{2}+2x-4x-8=16$

$x^{2}-2x-8-16=0$

$x^{2}-2x-24=0$

Step 2

Find the factored form

we have

$x^{2}-2x-24=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2}-2x=24$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2}-2x+1=24+1$

$x^{2}-2x+1=25$

Rewrite as perfect squares

$(x-1)^{2}=25$

Square root both sides

$(x-1)=(+/-)5$

$x=1(+/-)5$

$x=1+5=6$

$x=1-5=-4$

therefore

the equation in factored form is equal to

$(x-6)(x+4)=0$

Step 3

Verify the statements

case A) The equation $x-4=16$ can be used to solve for a solution of the given equation

The statement is False

Because , If you solve the equation

$x-4=16\\x=16+4 \\x=20$

The value of $x=20$ is not a solution--------> see the procedure

case B) The standard form of the equation is $x^{2}-2x-8=0$

The statement is False

Because the standard form is equal to $x^{2}-2x-24=0$

See the procedure

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

The statement is True

See the procedure

case D) One solution of the equation is $x=-6$

The statement is False

Because the solutions of the equation are $x=6$ and $x=-4$

See the procedure