Question

Is x - 8 a factor of the function f(x) = -2x3 + 17x2 - 64? Explain.

Answer 1

x-8=0
x=8
f(8)=-2(8)^3 +17(8)^2 - 64
=-2(512) + 17(64) - 64
= -1024+1088-64
= -1024 -64+1088
= -1088+1088
=0

so, x-8 is a factor of the function f(x) = -2x3 +17x2 - 64

hope this helps!!!!!! ^_^_^

Answer 2

we know that

If
`(x-8)` is a factor of the function
`f(x)=-2x^(3)+17x^(2)-64`

then

`x=8` is a root of the function f(x)

therefore

For
`x=8` the value of the function must be zero

Verify

Substitute the value of
`x=8` in the function

`f(8)=-2(8)^(3)+17(8)^(2)-64`

`f(8)=-2(512)+17(64)-64`

`f(8)=-1,024+1,088-64`

`f(8)=-1,088+1,088`

`f(8)=0`

therefore

the answer is

Yes,
`(x-8)` is a factor of the function f(x)