Show all work to factor x4 – 17x2 + 16 completely.
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Answer:
(x - 4)(x + 4)(x - 1)(x + 1)
Step-by-step explanation:
Given
[tex]x^{4}[/tex] - 17x² + 16
Use the substitution u = x², then
u² - 17u + 16
Consider the factors of the constant term (+ 16) which sum to give the coefficient of the u- term (- 17)
The factors are - 16 and - 1, then
u² - 17u + 16
= (u - 16)(u - 1) ← replace u by x²
= (x² - 16)(x² - 1) ← both factors are difference of squares
= (x - 4)(x + 4)(x - 1)(x + 1)
Answer: -18
Step-by-step explanation: x4-17x2+16= -18
i am not completely sure but here. i hope this helps god bless