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if you know that -2 is a zero of f left parenthesis x right parenthesis space equals space x cubed plus 7 x squared plus 4 x minus 12 , explain how to solve the equation x cubed plus 7 x squared plus 4 x minus 12 equals 0 . use complete sentences and proper grammar.

If you know that -2 is a zero of f(x) = x^3 + 7x^2 + 4x - 12, explain how to solve the equation.

First you have to figure out what could make f(x) = 0 to get rid of the cube. I'm going to test the array of data, x = -2, x = -3, and x = -4 because this type of equation probably has more negative values given that if you plug in some values the cubed-values and squared-values will surpass the "-12". Plug this into a calculator.
x^3 + 7x^2 + 4x - 12
f(-2) = -8 + 28 - 8 - 12 = 0

So you know that when x = -2, f(x) = 0. Divide "(x + 2)" from the equation and you will get... x^2 + 5x - 6. Now this is a simple polynomial one that you can figure to be (x + 6) (x - 1) just by looking at it because -6 multiplied by 1 is negative 6 and you see 5 and know that 6 - 1 = 5.

The solution is (x + 6) (x - 1) (x + 2) meaning that when x = -6, 1, or -2, f(x) is 0.

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