1. Create a class Polynomial that is used to evaluate a
polynomial
function
of
x:
P(x) 5
a0 1
a1x
1
a2x
1
. . .
1
an
2 1xn
2 1 1
anxn
The
coefficients
ai
are floating-point numbers, the exponents of
x
are integers,
and the largest exponent
n—called the
degree
of the polynomial—is
greater than or equal to 0. The class has the attributes
• degree—the value of the largest exponent
n
• coefficients—an array of the coefficients
ai
and the following methods:
• Polynomial(max)—a constructor that creates a polynomial of degree max
whose coefficients are all 0
• setConstant(i, value)—sets the coefficient
ai
to value
• evaluate(x)—returns the value of the polynomial for the given value x
For example, the polynomial
P(x) 5 3 1 5x
1 2x3
is of degree 3 and has coefficients
a0 5 3,
a1 5 5,
a2 5 0, and
a3 5 2. The
invocation evaluate(7) computes 3 1 5 3 7 1 0 3 7 1 2 3 73, which is
3 1 35 1 0 1 686, and returns the result 724.