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Advanced Math / Nonlinear functions Difficulty: Hard

h of x equals, x cubed plus, a, x squared, plus b x, plus c

The function h is defined above, where a, b, and c are integer constants. If the zeros of the function are negative 5 6, and 7, what is the value of c ?

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Explanation

The correct answer is 210. Since negative 5, 6, and 7 are zeros of the function, the function can be rewritten as h of x equals, open parenthesis, x plus 5, close parenthesis, times, open parenthesis, x minus 6, close parenthesis, times, open parenthesis, x minus 7, close parenthesis. Expanding the function yields h of x equals, x cubed, minus 8, x squared, minus 23 x, plus 210. Thus, a, equals negative 8, b equals negative 23, and c equals 210. Therefore, the value of c is 210.