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# Is x - 8 a factor of the function f(x) = -2x^{3} + 17x^{2} - 64? Explain.

**Solution: **

We can check x - 8 is a factor of f(x) = -2x^{3} + 17x^{2} - 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) = -2x^{3} + 17x^{2} - 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) = -2x^{3} + 17x^{2} - 64? Explain.

**Summary:**

x - 8 is a factor of the function f(x) = -2x^{3} + 17x^{2} - 64. Here we have verified both by synthetic division and long division method.

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