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A polynomial 
p has zeros when 
x=-2,x=(1)/(3), and 
x=3.
What could be the equation of 
p ?
Choose 1 answer:
(A) 
p(x)=(x+2)(x+3)(3x+1)
(B) 
p(x)=(x+2)(x+3)(3x-1)
(C) 
p(x)=(x+2)(x-3)(3x-1)
(D) 
p(x)=(x-2)(x+3)(3x+1)

A polynomial p p has zeros when x=2,x=13 x=-2, x=\frac{1}{3} , and x=3 x=3 .\newlineWhat could be the equation of p p ?\newlineChoose 11 answer:\newline(A) p(x)=(x+2)(x+3)(3x+1) p(x)=(x+2)(x+3)(3 x+1) \newline(B) p(x)=(x+2)(x+3)(3x1) p(x)=(x+2)(x+3)(3 x-1) \newline(C) p(x)=(x+2)(x3)(3x1) p(x)=(x+2)(x-3)(3 x-1) \newline(D) p(x)=(x2)(x+3)(3x+1) p(x)=(x-2)(x+3)(3 x+1)

Full solution

Q. A polynomial p p has zeros when x=2,x=13 x=-2, x=\frac{1}{3} , and x=3 x=3 .\newlineWhat could be the equation of p p ?\newlineChoose 11 answer:\newline(A) p(x)=(x+2)(x+3)(3x+1) p(x)=(x+2)(x+3)(3 x+1) \newline(B) p(x)=(x+2)(x+3)(3x1) p(x)=(x+2)(x+3)(3 x-1) \newline(C) p(x)=(x+2)(x3)(3x1) p(x)=(x+2)(x-3)(3 x-1) \newline(D) p(x)=(x2)(x+3)(3x+1) p(x)=(x-2)(x+3)(3 x+1)
  1. Identify Zeros: Zeros are x=2x=-2, x=13x=\frac{1}{3}, and x=3x=3. The factors of p(x)p(x) will be (x+2)(x+2), (x13)(x-\frac{1}{3}), and (x3)(x-3).
  2. Eliminate Fraction: To get rid of the fraction in the second factor, multiply by 33 to get 3(x13)3(x-\frac{1}{3}) which simplifies to (3x1)(3x-1).
  3. Formulate Equation: The equation of pp is p(x)=(x+2)(3x1)(x3)p(x)=(x+2)(3x-1)(x-3).
  4. Match with Options: Match the equation with the given options. The correct option is (C) p(x)=(x+2)(x3)(3x1)p(x)=(x+2)(x-3)(3x-1).

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