Question the-fu

2.2 Nonlinear Equations in One Variable - Quadratic solving (factoring, quadratic formula, completing square)
0:00

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 ?

Enter your answer:

The function h is defined above, where a , b , and c are integer constants.

Hard-difficulty · SAT Math · Nonlinear Equations in One Variable — Quadratic solving (factoring, quadratic formula, completing square). Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer 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.