Answer: The answer is YES.
Step-by-step explanation: We are given to check whether (x - 8) is a factor of the function [tex] f(x)=-2x^3+17x^2-64.[/tex]
Factor Theorem states that if (x - a) is a factor of P(x), the we must have P(a) = 0.
We have
[tex] f(8)\\\\=-2\times 8^3+17\times 8^2-64\\\\=-2\times 512+17\times 64-64\\\\=-2048+16\times 64\\\\=-1024+1024\\\\=0.[/tex]
Thus, (x - 8) is a factor of f(x).
x - 8 is a factor of f(x) = −2x³ + 17x² − 64, since f(8) = 0.
Polynomial is an expression involving the operations of addition, subtraction, multiplication of variables.
Types of polynomials are quadratic, linear, cubic and so on.
The factor theorem states that; when f(k) = 0, then (x – k) is a factor of f(x).
Hence to prove that x - 8 is a factor of f(x) = −2x³ + 17x² − 64, then f(8) = 0. Hence:
f(8) = -2(8)³ + 17(8)² - 64 = 0
Hence, x - 8 is a factor of f(x) = −2x³ + 17x² − 64, since f(8) = 0.
Find out more at: https://brainly.com/question/12787576.
