Question

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

Answer 1

Answer: The answer is YES.

Step-by-step explanation: We are given to check whether (x - 8) is a factor of the function $f(x)=-2x^3+17x^2-64.$

Factor Theorem states that if (x - a) is a factor of P(x), the we must have P(a) = 0.

We have

$f(8)\\\\=-2\times 8^3+17\times 8^2-64\\\\=-2\times 512+17\times 64-64\\\\=-2048+16\times 64\\\\=-1024+1024\\\\=0.$

Thus, (x - 8) is a factor of f(x).

Answer 2

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