Answered

Given that f, of, x, equals, x, squared, plus, 6, x, minus, 27f(x)=x
2
+6x−27 and g, of, x, equals, x, minus, 3g(x)=x−3, find f, of, x, dot, g, of, xf(x)⋅g(x) and express the result as a polynomial in simplest form.



Answer :

sqdancefan

Answer:

  x³ +3x² -45x +81

Step-by-step explanation:

You want the simplified form of f(x)·g(x) when ...

  • f(x) = x² +6x -27
  • g(x) = x -3.

Product

The product of the two functions is ...

  f(x)·g(x) = (x² +6x -27)·(x -3)

  = x(x² +6x -27) -3(x² +6x -27)

  = x³ +6x² -27x -3x² -18x +81

  = x³ +(6 -3)x² +(-27-18)x +81

  f(x)·g(x) = x³ +3x² -45x +81

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