Answer:
a) y = 2x⁴ -18x² +8x +24
b) 4th degree; tends toward +∞ when |x| gets large
Step-by-step explanation:
a) When r is a root of the polynomial, (x -r) is a factor. The given roots mean the factors are ...
y = a(x -(-1))(x -(-3))(x -2)(x -2) = a(x+1)(x+3)(x-2)²
The product of the constant terms is a(1)(3)(2²) = 12a. This is the y-intercept, which is said to be 24. So ...
12a = 24 ⇒ a = 2
The polynomial function is then ...
y = 2(x +1)(x +3)(x -2)²
y = 2x⁴ -18x² +8x +24
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b) The leading coefficient of this 4th-degree polynomial is positive, so when x has large positive or negative values, the function value will tend toward positive infinity.
