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)