haydenjp01 haydenjp01
  • 10-06-2019
  • Mathematics
contestada

If f(x)=x^4-x^3+x^2 and g(x)=-x^2, where x =/= 0, what is (f/g)(x)?

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jimrgrant1 jimrgrant1
  • 10-06-2019

Answer:

- x² + x - 1

Step-by-step explanation:

(f / g)(x)

= [tex]\frac{x^4-x^3+x^2}{- x^2}[/tex]

divide each term on the numerator by - x²

= [tex]\frac{x^4}{- x^2}[/tex] - [tex]\frac{x^3}{-x^2}[/tex] + [tex]\frac{x^2}{-x^2}[/tex]

=  - [tex]x^{4-2}[/tex] + [tex]x^{3-2}[/tex] - [tex]x^{2-2}[/tex]

= - x² + x - [tex]x^{0}[/tex] = - x² + x - 1

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