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

Select statements 2 and 4.

- Step 2: x^4 − 32x^2 + 56 = −200 → x^4 − 32x^2 + 256 = 0 — this is adding 200 to both sides (Addition Property of Equality).
- Step 4: (x^2 − 16)^2 = 0 → ((x + 4)(x − 4))^2 = 0 — this uses the difference of squares to factor x^2 − 16.

(Step 1 is subtraction of 20x^2, not multiplication; Step 3 is factoring a perfect square trinomial into (x^2 − 16)^2, not the difference of squares.)