Question

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.

Answer 1

Answer:

3rd statement

Step-by-step explanation:

Lets go through the choices and see.

The first one says:

The equation x – 4 = 16 can be used to solve for a solution of the given equation.

If we solve this we get x=20. I just added 4 on both sides.

Is 20 a solution thr original equation? Let's check. We need to replace x with 20 in

(x – 4)(x + 2) = 16 to check.

(20-4)(20+2)=16

(16)(22)=16

16 times 22 is definitely not equal to 16 so the first statement is false.

Lets check option 2:

The standard form of the equation is

x2 – 2x – 8 = 0.

So lets put our equation in standard form and see:

(x – 4)(x + 2) = 16

Foil is what we will use:

First: x(x)=x^2

Inner: (-4)x=-4x

Outer: x(2)=2x

Last: -4(2)=-8

Add together to get: x^2-2x-8. We still have the equal 16 part.

So the equation is now x^2-2x-8=16. Subtracting 16 on both sides will put the equation in standard form. This gives us

x^2-2x-24=0. This is not the same as the standard form suggested by option 2 in our choices.

Checking option 3:

This says:

The factored form of the equation is

(x + 4)(x – 6) = 0.

So we already put our original equation in standard form. Lets factor our standard form and see if is the same as option 3 suggests.

To factor x^2-2x-24, we need to find two numbers that multiply to be -24 and add to be -2. These numbers are 4 and -6 because 4(-6)=-24 and 4+(-6)=-2. So the factored form of our equation is (x+4)(x-6)=0 which is what option 3 says. So option 3 is true.

Let's go ahead and check option 4: It says: One solution of the equation is x = –6. This is false because solving (x+4)(x-6)=0 gives us the solutions x=-4 and x=6. Neither one of those is -6. *

* I solved (x+4)(x-6)=0 by setting both factors equal to zero and solving them for x. Like so,

x+4=0 or x-6=0.

Answer 2

Answer:

Factored form...

Step-by-step explanation:

Foil out (x-4)(x+2)=16

First: x*x=$x^{2}$

Outer: 2*x=2x

Inner: -4*x = -4x

Last: -4*2 = -8

Combine them all:

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

Simplify:

$x^2-2x-8=16\\x^2-2x-24=0$

What multiplies together to make -24 but adds together to make -2?

Lets list the factors of -24 to decide:

1 x -24

2 x -12

3 x -8

4 x -6

-6+4 = -2

Therefore...

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