Is x - 8 a factor of the function f(x) = -2x3 + 17x2 - 64? Explain.
Solution:
We can check x - 8 is a factor of f(x) = -2x3 + 17x2 - 64 using synthetic division method i.e. by synthetic division if the remainder is zero then x - 8 is a factor of given f(x) otherwise it is not.
The remainder is 0
Since remainder is zero, x - 8 is a factor of given f(x)
ALITER:
We can use the long division method to check x - 8 is a factor of f(x). Again here by long division if remainder is zero then x - 8 is a factor otherwise it is not, process of long division is as follows
Since remainder is zero x - 8 a factor of given f(x)
Aliter
If x - 8 is a factor of f(x) then (x - 8) = 0 ⇒ x = 8
Here, f(8) must be equal to zero.
f(x) = -2x3 + 17x2 - 64
f(8) = -2(8)3 + 17(8)2 - 64
= -1024 + 1088 - 64
= 0
Therefore, x - 8 is a factor of f(x)
Is x - 8 a factor of the function f(x) = -2x3 + 17x2 - 64? Explain.
Summary:
x - 8 is a factor of the function f(x) = -2x3 + 17x2 - 64. Here we have verified both by synthetic division and long division method.