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 e

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.

in progress 0
Lydia 2 weeks 2021-09-10T22:47:05+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T22:48:27+00:00

    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

    0
    2021-09-10T22:48:31+00:00

    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.

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )