Question

Is x − 8 a factor of the function f(x) = −2x³ 17x² − 64? explain.

Option 1: Yes, when the function f(x) = −2x³ 17x² − 64 is divided by x − 8, the remainder is zero. therefore, x − 8 is a factor of f(x) = −2x³ 17x² − 64.
Option 2: No, when the function f(x) = −2x³ 17x² − 64 is divided by x − 8, the remainder is zero. therefore, x − 8 is not a factor of f(x) = −2x³ 17x² − 64.
Option 3: Yes, when the function f(x) = −2x³ 17x² − 64 is divided by x − 8, the remainder is not zero. therefore, x − 8 is a factor of f(x) = −2x³ 17x² − 64.
Option 4: No, when the function f(x) = −2x³ 17x² − 64 is divided by x − 8, the remainder is not zero. therefore, x − 8 is not a factor of f(x) = −2x³ 17x² − 64.

Answer 1

Substituting x = 8 into f(x) yields f(8) = 0, confirming that x - 8 is a factor of the polynomial f(x) = -2x^3 + 17x^2 - 64 according to the Remainder Theorem.

Step-by-step explanation:

To determine if x − 8 is a factor of the function f(x) = −2x³ + 17x² − 64, we can use the Remainder Theorem. According to this theorem, for a given polynomial f(x), if f(a) = 0 for some value a, then x - a is a factor of the polynomial.

Let's substitute x = 8 into the function f(x) and see if the result is zero:

• f(8) = −2(8)³ + 17(8)² − 64
• f(8) = −2(512) + 17(64) − 64
• f(8) = −1024 + 1088 − 64
• f(8) = 0

Since f(8) = 0, x − 8 is indeed a factor of the polynomial f(x) = −2x³ + 17x² − 64. Therefore, the correct choice is: Yes, when the function f(x) = −2x³ + 17x² − 64 is divided by x − 8, the remainder is zero. Hence, x − 8 is a factor of f(x).