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Amy is solving the equation using the steps shown.



Which could be the correct next step in solving the equation?


Subtract 2 from both sides of the equation to yield (x 2 – 16) = 0.
Subtract 2 from both sides of the equation to yield (, x , 2, – 16) = 0.

Multiply (x 2 – 16)(x + 2) on the left side of the equation to yield x 3 + 2x 2 – 16x – 32 = 0.
Multiply (, x , 2, – 16)(, x, + 2) on the left side of the equation to yield , x, , 3, + 2, x, , 2, – 16, x, – 32 = 0.

Factor (x 2 – 16) on the left side of the equation to yield (x + 4)(x – 4)(x + 2) = 0.
Factor (, x , 2, – 16) on the left side of the equation to yield (, x, + 4)(, x, – 4)(, x, + 2) = 0.

Add 16 to both sides of the equation to yield x 2(x + 2) = 0.
Add 16 to both sides of the equation to yield , x , 2, (, x, + 2) = 0.

Sagot :

MrRoyalidn

The correct next step Amy could take is to factor (x^2 - 16) on the left side of the equation to yield (x + 4)(x – 4)(x + 2) = 0.

The equation is given as:

[tex]\mathbf{(x^2 - 16)(x + 2) = 0}[/tex]

The possible next steps are:

1. Expand the equation as follows

[tex]\mathbf{x^3+2x^2-16x-32 = 0}[/tex]

2. Express x^2 -16 as a difference of two squares as follows

[tex]\mathbf{(x + 4)(x- 4)(x + 2) = 0}[/tex]

However, the correct step in this case is to factor x^2 - 16 as a difference of two squares to give [tex]\mathbf{(x + 4)(x- 4)(x + 2) = 0}[/tex]

This is so, because the question says Amy is trying to solve for variable x.

This step will ensure that she gets the possible values of x, unlike expanding the whole equation .

Hence, the correct next step is [tex]\mathbf{(x + 4)(x- 4)(x + 2) = 0}[/tex]

Read more about equations at:

https://brainly.com/question/7674413

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