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.
