Answer:
a) x = {-2, 1, 3} are the zeros
b) y = (x +2)(x -1)(x -3)
c) y = x^3 -2x^2 -5x +6
Step-by-step explanation:
a) The zeros are the values of x where the graph crosses y=0. Those values are x = -2, x = 1, x = 3.
__
b) If "a" is a zero, then (x-a) is a factor. The factored polynomial is ...
y = (x +2)(x -1)(x -3)
__
c) This can be multiplied out using the distributive property several times.
y = (x +2)(x(x -3) -1(x -3))
= (x +2)(x^2 -3x -x +3)
= (x +2)(x^2 -4x +3)
= x(x^2 -4x +3) +2(x^2 -4x +3)
= x^3 -4x^2 +3x +2x^2 -8x +6
y = x^3 -2x^2 -5x +6
_____
The supplied graph apparently scales this vertically by a factor of 1/2, since its y-intercept is at (0, 3), not (0, 6).
