Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation 
), and factor f(x) into linear factors.f(x) = x4 + 12x3 + 31x2 - 12x - 32
A. -8, -4, 1, multiplicity 2; f(x) = (x + 8)(x + 4)(x - 1)2
B. -4, -1, 1, 8; f(x) = (x + 4)(x + 1)(x - 1)(x - 8)
C. -1, 1, 4, 8; f(x) = (x + 1)(x - 1)(x - 4)(x - 8)
D. -8, -4, -1, 1; f(x) = (x + 8)(x + 4)(x + 1)(x - 1)
Answer: D
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Find the volume of the solid generated by revolving the region R bounded by the graphs of the given equations about the y-axis.x = 3y - y2, x = 0
A. 
?
B. 
?
C. 
?
D. 
?
Simplify the expression by combining like terms.-0.2y - 8 - 2y + 3.1
A. 0.4y - 24.8 B. -2.2y - 4.9 C. -0.2y - 2y - 8 + 3.1 D. -7.1
Simplify the expression.-4-2
A. - 
B. 
C. -16
D. 16
Provide an appropriate response.Explain the idea of a related rate.
A. A function y = f(x) is a function of x, but if x can be expressed as a function of some other variable, such as time, t, then y is also a function of t, and the dependence of y on t is related to the dependence of x on t, which means, in turn, that the rate of change of y, dy/dt, is related to the rate of change of x, dx/dt, by the relation 
= 
? 
.
B. A function y = f(t) is a function of t, but y can generally be related to x if x is also a function of t; that is, dy/dt ? dx/dt.
C. A function x = f(t) is a function of t, but x can generally be related to y if y is also a function of t; that is, dx/dt ? dx/dy.
D. A function y = f(x) is a function of x, but if x can be expressed as a function of some other variable, such as time, t, then y is also a function of t, and the dependence of y on t is related to the dependence of x on t, which means, in turn, that the rate of change of y, dy/dt, is related to the rate of change of x, dx/dt, by the relation 
= 
? 
.