Question

Which of the following options is a linear factor of the expression x4−8x2−9
𝑥
4
−
8
𝑥
2
−
9
?(1 point)
Responses

(x−2)
(
𝑥
−
2
)
open paren x minus 2 close paren

(x−1)
(
𝑥
−
1
)
open paren x minus 1 close paren

(x−3)

Answer 1

To determine which of the given options is a linear factor of the expression \( x^4 - 8x^2 - 9 \), we can evaluate the expression at the potential roots from the options provided: \( x - 2 \), \( x - 1 \), and \( x - 3 \).

1. **Test \( x = 2 \)**:
\[
f(2) = 2^4 - 8(2^2) - 9 = 16 - 32 - 9 = -25 \quad (\text{not a root})
\]

2. **Test \( x = 1 \)**:
\[
f(1) = 1^4 - 8(1^2) - 9 = 1 - 8 - 9 = -16 \quad (\text{not a root})
\]

3. **Test \( x = 3 \)**:
\[
f(3) = 3^4 - 8(3^2) - 9 = 81 - 72 - 9 = 0 \quad (\text{is a root})
\]

Since \( f(3) = 0 \), \( (x - 3) \) is a linear factor of the expression \( x^4 - 8x^2 - 9 \).

Therefore, the correct answer is:
\[
(x - 3)
\]