Is x + 10 a factor of the function f(x) = x³ - 75x + 250? Explain.

Solution:

Given:

Function f(x) = x³ - 75x + 250

We can make use of the factor theorem to find if x + 10 is a factor of the given function

The factor theorem states that x - a is a factor of f(x) if and only if f(a) = 0

x + 10 is a factor f(-10) = 0

We know that

f(x) = x³ - 75x + 250

Let us take x as -10

f(-10) = (-10)³ - 75(-10) +250

By further calculation, we get

f(-10) = -1000 + 750 + 250

f(-10) = 0

Therefore, x + 10 is a factor of the function f(x) = x³ - 75x + 250.

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Is x + 10 a factor of the function f(x) = x³ - 75x + 250? Explain.

Summary:

Yes, x + 10 a factor of the function f(x) = x³ - 75x + 250 using the factor theorem.