Question

((Look at the image))

Answer 1

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.