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A polynomial function has a zero at x = 1 with a multiplicity of 3 and a zero at x = -2 with a multiplicity of 1. The y – intercept for the function is (0, -8). Write an equation for this polynomial.

Answer :

SQDANCEFANGO

Answer:

  f(x) = 4(x -1)^3·(x +2)

Step-by-step explanation:

Each root x=p indicates the function has a factor (x -p). The factor will be repeated according to the multiplicity of the root.

  f(x) = a(x -1)^3·(x +2)

  f(0) = a(-1)^3·2 = -2a = -8   ⇒   a = 4

The factored form of the equation is ...

  f(x) = 4(x -1)^3·(x +2)

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