For the function f(x) = x3 + 3x2 – 70x – 144, f(–9) = 0, f(–2) = 0, and f(8) = 0. what are the solutions to the equation x3 + 3x2 = 70x + 144?

a) x = –8, x = 2, and x = 9
b) x = –9, x = –2, and x = 8
c) x = –8, x = –2, and x = 9
d) x = –9, x = –8, and x = –2

Option B). x = -9, -2 and 8.

Step-by-step explanation:

The given function is f(x) = x³ + 3x² -70x - 144 and f(-9) = 0, f(-2) = 0, f(8) = 0

We have to find the solutions to the equation x³+ 3x² = 70x + 144

Now we rewrite the function in the equation form as

x³ + 3x² - 70x - 144 = 0

x³ + 3x² = 70x + 144

we know for the values of x = -9, -2, and 8 value of the function is 0. So when we rewrite the function in the form of an equation,  -9, -2 and 8 will be the zero factors of the equation.

So solutions of the equation are x = -9, -2 and x = 8.

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