Question

Quentin solved the polynomial equation
x
4
−
12
x
2
+
56
=
20
x
2
−
200
using the steps shown below.

x
4
−
32
x
2
+
56
=
−
200
x
4
−
32
x
2
+
256
=
0
(
x
2
−
16
)
2
=
0
(
(
x
+
4
)
(
x
−
4
)
)
2
=
0

(
x
+
4
)
(
x
−
4
)
(
x
+
4
)
(
x
−
4
)
=
0
x
=
−
4
,
4
Select TWO statements that correctly justify the steps of Quentin's solution process.


Step 1 applies the Multiplication Property of Equality.


Step 2 applies the Addition Property of Equality.


Step 3 applies the difference of squares formula to factor the expression.


Step 4 applies the difference of squares formula to factor the expression inside the parentheses.

Answer 1

Correct choices:
- Step 2 applies the Addition Property of Equality.
- Step 4 applies the difference of squares formula to factor the expression inside the parentheses.

Reason: Step 2 is obtained by adding 200 to both sides (an addition to both sides). Step 4 factors x^2 − 16 as (x+4)(x−4), which is the difference of squares. Step 3 is a perfect-square factorization, not a difference of squares, and Step 1 is not multiplication.